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abelian surface; good reduction of curves few rational points of Shimura curve; imaginary quadratic number field; quaternionic multiplication; QM-abelian surfaces; potential good reduction
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abelian surface; good reduction of curves moduli space of complete smooth curves; principally polarized abelian varieties; Torelli theorem; Schottky problem; Kummer surface of the Jacobian; theta constants; K-P equation
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abelian surface; good reduction of curves abelian surfaces; number fields; good reduction; elliptic curves
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abelian surface; good reduction of curves moduli space of curves; covering of the elliptic curve; Jacobian; Humbert surface; moduli space of principally polarized abelian surfaces; period matrix
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abelian surface; good reduction of curves Riemann surface; moduli space of semistable vector bundles on curves; non-abelian theta-function; determinant line bundle; theta divisor; trisecant identity
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abelian surface; good reduction of curves Galois modules of finite commutative group schemes; ring of Witt vectors; abelian varieties with good reduction everywhere over the; rationals; nontrivial p-divisible groups over the integers; abelian varieties with good reduction everywhere over the rationals
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abelian surface; good reduction of curves characteristic \(p\); good reduction; constructing unramified coverings of the affine line; modular curves; Galois groups of unramified coverings of the affine line; Klein curve; Macbeath curve; big automorphism groups; Jacobian varieties
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abelian surface; good reduction of curves degeneration of weight spectral sequence; good reduction of abelian variety; weight filtration; mixed crystal; duality pairing; abelian variety
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abelian surface; good reduction of curves geometric genus; irregularity; rational equivalence classes of zero cycles; pseudo-rational surface; very good reduction
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abelian surface; good reduction of curves product of elliptic curves; abelian surface
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abelian surface; good reduction of curves characteristic \(p\); Galois group of number fields of curves; elliptic curve; potentially good reduction
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abelian surface; good reduction of curves abelian differential; translation surface; moduli space of curves; limit linear series; spin structure; admissible cover; Weierstrass point
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abelian surface; good reduction of curves Siegel modular group; resolution of cusps; rational Hilbert modular surfaces; canonical maps; modular curves; intersection theory; moduli spaces; abelian varieties with real multiplication; Kummer surface
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abelian surface; good reduction of curves abelian variety; elliptic curve; Hasse invariant; Artin effect; infiniteness of Tate-Shafarevich group; quasi-global field; potentially good reduction; Neron minimal models
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abelian surface; good reduction of curves nonexistence of abelian varieties; good reduction; conjecture of Shafarevich; Néron models
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abelian surface; good reduction of curves abelian surface; holomorphic curve; number of curves; Gromov-Witten invariants
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abelian surface; good reduction of curves covering of stable genus three curves; fibre of Prym map; abelian surface; symmetric theta divisor; Satake compactification of the moduli space of principally polarized abelian surfaces
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abelian surface; good reduction of curves abelian surface; singluarities of curves; curves of low genus; isogeny; Jacobian variety; nonprimitive polarization
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abelian surface; good reduction of curves intersection; curves on abelian branched covering of smooth complex projective surface; Betti numbers; desingularizations
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abelian surface; good reduction of curves isogenous Jacobian varieties; equivalence classes of curves; Weierstrass points; good reduction
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abelian surface; good reduction of curves Colmez conjecture; Siegel zero; Faltings height; CM abelian varieties; Artin \(L\)-function; good reduction of abelian varieties
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abelian surface; good reduction of curves numbers of nodal curves; numbers of curves on a K3 surface; genus 2 curves an an abelian surface; Hilbert schemes of points
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abelian surface; good reduction of curves number of rational curves on a quartic surface in \(\mathbb{P}_ 3\); principally polarized abelian surfaces; quartic surfaces
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abelian surface; good reduction of curves period matrix; Riemann surfaces; homomorphism between the homotopy groups; surface map; reduction of abelian integrals; homomorphism of abelian varieties; principal polarization of the Jacobian
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abelian surface; good reduction of curves elliptic curves; good reduction; global minimal model; diophantine equations; effective procedure; real quadratic field; number of isomorphism classes; 2-division point; table
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abelian surface; good reduction of curves elliptic curves over finite fields; Weil conjectures; group of torsion; elliptic curves over local fields; good reduction; elliptic curves over global fields; Mordell-Weil theorem; descent; Selmer group; Shafarevich groups
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abelian surface; good reduction of curves abelian surfaces; \(L\)-function; bad reduction; \(l\)-adic cohomology; K3 surface; dimension of fourth cohomology group
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abelian surface; good reduction of curves \(p\)-adic \(L\)-functions; \(p\)-adic heights; global Zeta-module of \(p\)-adic \(L\)-functions; \(p\)-adic Birch and Swinnerton-Dyer formulas; Iwasawa theory of abelian varieties; good non-ordinary reduction; tower of local points; splitting of the Hodge filtration; lower bound; Selmer groups
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abelian surface; good reduction of curves number of elliptic curves; good reduction; conductor; elliptic factors of the modular Jacobian
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abelian surface; good reduction of curves automorphisms of curves; Hurwitz bound; good reduction
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abelian surface; good reduction of curves Grothendieck standard conjecture; fourfolds; abelian schemes; standard conjecture of Lefschetz type; Néron minimal model; reduction of multiplicative type; \(K3\) surface; hyperkähler variety; Chow-Lefschetz decomposition; Abel-Jacobi map
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abelian surface; good reduction of curves abelian differential; translation surface; moduli space of curves; affine invariant submanifold; Teichmüller curve; Siegel-Veech constant; Lyapunov exponent; quadratic differential
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abelian surface; good reduction of curves moduli spaces of algebraic curves; free fermions over a compact Riemann surface; soliton equations; theta functions; cobordism theory; formal groups; non-abelian conformal field theory; conformal block; gauge symmetries
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abelian surface; good reduction of curves equivalence classes of curves; rational Weierstrass point; good reduction; isogeny classes
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abelian surface; good reduction of curves Iwasawa theory; norm subgroup of formal group; \({bbfZ}_ p\)-extension; formal Lie group; Cartier duality; abelian variety with good reduction; p-divisible group; cyclotomic \({bbfZ}_ p\)-extension; infinite dimensional formal Lie group of Witt covectors; Dieudonné modules
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abelian surface; good reduction of curves eigenvalues of Hecke operators; modular symbols method; computation of cusp forms; elliptic curves; verification of a conjecture of Stevens on modular curves; elliptic curves with everywhere good reduction; minimal period lattice
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abelian surface; good reduction of curves fields of moduli; action of automorphism of reflex field on the torsion points; Abelian varieties with many complex multiplications; Abelian variety; cyclotomic fields; primes of good reduction; prime ideal decomposition of the endomorphism; Frobenius map; Riemann forms; field of definition; rank of a CM type; Langlands' conjecture; size of the Galois group of torsion points
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abelian surface; good reduction of curves no elliptic curves with good reduction everywhere group of units; cubic ground field
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abelian surface; good reduction of curves elliptic curves with complex multiplication; curves of genus 2; Jacobians; product surfaces; abelian variety; Humbert invariant; binary and ternary quadratic forms; idoneal numbers; mass formula
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abelian surface; good reduction of curves \(K\)-group; semi-abelian varieties; product of curves over a finite field
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abelian surface; good reduction of curves non commutative algebraic geometry; surface; blow up; graded algebras of Gelfand-Kirillov dimension three; Abelian categories; Rees algebra; pseudo-compact rings; completion functors; derived categories; Del Pezzo surfaces; quantum version of projective three space
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abelian surface; good reduction of curves étale \(p\)-covers; torsionless fundamental group; group acting on scheme; \(p\)-ranks of smooth projective curves; characteristic \(p\); Euler-Poincaré characteristic; singular Enriques surface
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abelian surface; good reduction of curves essential dimension; stack; gerbe; moduli of curves; moduli of abelian varieties
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abelian surface; good reduction of curves curves over finite fields; zeta-functions of curves; Abelian varieties over finite fields
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abelian surface; good reduction of curves \(C_{ab}\) curves; Jacobian variety; addition of divisors; reduction algorithms; intersections in projective space
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abelian surface; good reduction of curves deformation theory; finite group schemes; abelian varieties; Newton polygons; automorphisms of algebraic curves
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abelian surface; good reduction of curves principally polarized abelian variety; symmetric theta divisor; Gauss map; Thom-Boardman loci; Jacobians of nonhyperelliptic curves
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abelian surface; good reduction of curves moduli space of curves and abelian varieties; geodesics; Prym locus; Jacobian locus; generalized Prym varieties; admissible coverings
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abelian surface; good reduction of curves Jacobian of a hyperplane section of a surface; endomorphisms of abelian varieties; Albanese variety; linear system
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abelian surface; good reduction of curves topology of real algebraic curves; algebraic curves depending on parameters; analytic dependence; Pfaffian chains; algebraic surface singularities
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abelian surface; good reduction of curves unirationality of moduli space of 5-dimensional principally; polarized abelian varieties; Prym moduli space parametrizing double covers of curves of; genus 6; nets of quadrics; theta characteristic; Prym moduli space parametrizing double covers of curves of genus 6
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abelian surface; good reduction of curves degenerations of Kummer surfaces; abelian surface; Nieto's quintic threefold; toroidal compactification of the Siegel modular threefold
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abelian surface; good reduction of curves semi-abelian varieties; Néron models; group of components; tame ramification; Weil restrictions; Tate curves; Jacobian varieties; swan conductor
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abelian surface; good reduction of curves surfaces of general type; \(p_g=0\); homology groups; products of curves; actions of finite abelian group; isotrivial fibrations; surfaces isogenous to a product; fake quadrics; branched coverings; fundamental group
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abelian surface; good reduction of curves Prym-Tyurin varieties; correspondence of a curve; Jacobian; subvariety of abelian variety; de Franchis' theorem; number of morphisms onto curves
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abelian surface; good reduction of curves Albanese variety; algebraic cycles; second cohomology group of a surface with prescribed singularities; curves on surfaces; effective divisor; 1- motive; periods
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abelian surface; good reduction of curves automorphisms of Abelian surfaces; Kummer surface; analog of Nikulin's theorem
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abelian surface; good reduction of curves curve on a \(K3\) surface; curves of high genus; Brill-Noether-Petri condition; linear series; surjectivity of the Wahl map
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abelian surface; good reduction of curves theta-divisor; principally polarized abelian variety; Kummer variety; Welters conjecture; Jacobians of curves
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abelian surface; good reduction of curves $K3$ surface; Severi variety; moduli space of curves
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abelian surface; good reduction of curves minimal free resolution of a canonically embedded curve; surface of general type; syzygies; fibration of curves; slope; Horikawa index; Clifford index
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abelian surface; good reduction of curves schemes; coherent sheaves; cohomology of schemes; duality theory; algebraic curves; birational geometry of surfaces; arithmetic algebraic curves; arithmetic algebraic surfaces; stable reduction of curves; arithmetic algebraic geometry; birational geometry of algebraic surfaces
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abelian surface; good reduction of curves curves on surfaces; minimal analytic surface; number of algebraic families of curves with fixed arithmetic genus
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abelian surface; good reduction of curves elliptic curves; isogenies; additive reduction; parameterized families of elliptic curves
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abelian surface; good reduction of curves elliptic curve; good reduction; point of order 2
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abelian surface; good reduction of curves torsion points of abelian varieties; product of non-isogenous elliptic curves
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abelian surface; good reduction of curves moduli space of curves; moduli space of abelian variety; monodromy
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abelian surface; good reduction of curves algebraic fundamental group; stack inertia; special loci; good groups; absolute Galois group; moduli space of algebraic curves; branched covering
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abelian surface; good reduction of curves \(K3\) surface; Severi variety; nodal curve; Hilbert scheme of nodal curves
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abelian surface; good reduction of curves higher Hasse-Witt matrices; formal group laws; length of a jump; sequence for abelian varieties; unit root crystal; hyperelliptic; curves
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abelian surface; good reduction of curves category of isogenies of principally polarized abelian schemes; bad reduction of Siegel moduli schemes with level structures; Drinfel'd level structure; full set of sections; Dieudonné theory
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abelian surface; good reduction of curves proof of Mordell conjecture; proof of Tate conjecture; proof of; Shafarevich conjecture; height of Abelian variety; rational points; on elliptic curves
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abelian surface; good reduction of curves characteristic \(p\); torus; Néron model; split reduction; elliptic curves; abelian varieties; Swan conductor
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abelian surface; good reduction of curves Hodge ring of an Abelian variety; divisor classes; Hodge conjecture; Hilbert modular surface
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abelian surface; good reduction of curves Hodge structure; Shimura variety; special subvarieties; Hodge structure of CM-type; $K3$-surface; surface of general type; domination by products of curves
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abelian surface; good reduction of curves Hurwitz inequality; coverings of curves; bounds for order of abelian subgroups of automorphism group of algebraic curve; characteristic p
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abelian surface; good reduction of curves Moduli of stable sheaves; Fourier-Mukai functor; \(K3\) surface; abelian surface
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abelian surface; good reduction of curves family of curves; semistable fiber; rational surface
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abelian surface; good reduction of curves rigid analytic group; stable reduction of abelian varieties; Raynaud representation
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abelian surface; good reduction of curves degeneration of complex curves; complex surface; singular fibre; Riemann surface; splitting of singular fibres; atomic degeneration
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abelian surface; good reduction of curves Calabi-Yau threefolds; unipotent monodromy; variation of the Hodge structure; Picard-Fuchs differential equation; K3 surfaces; elliptic curves; product of a \(K3\) surface and an elliptic curve
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abelian surface; good reduction of curves Chowla's conjecture; \(L\)-functions; zeta functions of curves; Carlitz extensions; cyclotomic function fields; abelian varieties over finite fields
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abelian surface; good reduction of curves surface of general type; abelian surface; Albanese map surface of general type; abelian surface; Albanese map
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abelian surface; good reduction of curves derived equivalences; quantum Hamiltonian reduction; microlocalization; Beilinson-Bernstein theory; hodge theory; localized derived category; quantum Hamiltonian reduction; chomological boundedness; wreath product; Cherednik algebras; right adjoint; left adjoin; microlocal derived categories; microlocal abelian categories; Serre duality of derived categories
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abelian surface; good reduction of curves vector bundles; conformal quantum field theory; Verlinde formula; Hilbert functions of moduli spaces of semi-stable vector bundles; compact Riemann surface; generalized theta bundle; Witten conjecture; intersection theory of moduli spaces of algebraic curves; topological field theories; fusion algebras
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abelian surface; good reduction of curves textbook (algebraic geometry); algebraic curves; projective varieties; abelian categories; schemes; cohomology of schemes; intersection theory; duality theory
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abelian surface; good reduction of curves good reduction; Newton polygon; abelian variety
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abelian surface; good reduction of curves survey; finite dimensional algebras; exceptional curves; noncommutative curves; exceptional sequences of coherent sheaves; weighted projective lines; module categories for canonical algebras; homogeneous curves; finite dimensional tame bimodule algebras; vector bundles with parabolic structures; coordinate algebras; surface singularities; tame hereditary algebras
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abelian surface; good reduction of curves abelian automorphism groups; surface of general type; genus 2 fibrations
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abelian surface; good reduction of curves tropical geometry; tropical curves; metric graphs; Torelli map; moduli of curves; abelian varieties
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abelian surface; good reduction of curves pencil of curves; del Pezzo surface; Hasse principle
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abelian surface; good reduction of curves moduli of curves; stable curve according to a cubic graph; Gaussian map; curve on a \(K3\) surface
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abelian surface; good reduction of curves General surface family of \(2^nd\) degree; orthogonal system; algebraic; concentric; rectangular; equation; parameter; O.D.E.; elimination resultant; Darboux; class of curves; cyclic; confocal
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abelian surface; good reduction of curves CM cycles; Shimura curves; Abel-Jacobi map in Hodge numbers; abelian surfaces with quaternionic multiplication; complex multiplication cycles; Griffiths group of infinite rank
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abelian surface; good reduction of curves curves on a surface; type of curve; Hilbert functions; 0-dimensional subschemes
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abelian surface; good reduction of curves abelian variety; cone of curves; Néron-Severi group; cone theorem
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abelian surface; good reduction of curves curves of genus 4; moduli space; reflection group; K3 surface
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abelian surface; good reduction of curves elliptic curves over an algebraic number field; Galois module of \(p\)-torsion points; height conjecture; asymptotic Fermat conjecture; principally polarized abelian variety; curves of genus 2
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abelian surface; good reduction of curves product of elliptic curves; principally polarized abelian surfaces; Jacobians; family of curves
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abelian surface; good reduction of curves homology of the spin moduli spaces of Riemann surfaces with spin structure; Arf invariant; spin mapping class groups; fermionic string theory; Picard group; configuration of simple closed curves on a surface
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