# Questions tagged [abelian-varieties]

Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.

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### Some basic questions on quotient of group schemes

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### Conceptual explanations of the class numbers for the first few $\mathbb{Q}(\sqrt{p})$ with odd conductor

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### For an abelian scheme, $R^pf_* \Omega^q$ is locally free and its formation is compatible with any base change

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### $\mathcal{M}_g$ and $\mathcal{A}_g$ have natural structures as quasi-projective varieties

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### Surjectivity of the Abel-Prym map

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### Polarization of an abelian variety made by the sum of two divisors

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### Homogeneous vector bundles on Abelian varieties

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### Isomorphism of certain irreducible representations over finite fields

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### A map on Jacobians coming from a correspondence explicitly

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### On the moduli stack of abelian varieties without polarization

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### Sections of infinite order of elliptic surfaces

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### For which (g,q) does there exist a supersingular curve?

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### Surfaces of general type with $q=1$

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### Proving the Immersion part of an Embedding

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### The profinite topology on the Mordell Weil group

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### A Lefschetz style formula for the $\ell^\infty$ torsion of an Abelian variety over a finite field

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### Chow variety of 1-cycles on abelian surface

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### Structure of non-big divisors in an abelian variety

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### Jacobian fibration of an abelian fibration

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### The Picard scheme of an ordinary singular curve

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### $A$ is a CM abelian variety over $\mathbb{C}$, $\sigma \in$ Aut$(\mathbb{C})$. How to define $\sigma A$?

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### When a CM abelian variety has complex multiplication by $\mathcal{O}_E$?

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### Elliptic curves and archimedean place

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### Uniqueness of theta divisor

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### Application of Galois descent

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### Nef divisors on abelian varieties are pullbacks of ample ones

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### Example of a non log-canonical pair for an abelian variety with polarization of degree >2

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### Good reduction of finite etale covers of abelian varieties

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### Why does MAGMA claim that the automorphism group of a curve is trivial?

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### Relation between elliptic curve and Fermat's last thereom

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### Compatiblity of completion and fibre products. (Formal completion and formal groups)

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### Isomorphic Jacobian Varieties Just Like Abelian Varieties — Torelli's Theorem

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### Tamagawa numbers

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### What are the genus 4 curves with Jacobians that are 4-th powers?

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### Lifting a splitting of an Abelian variety to characteristic 0

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### Genus two curves on abelian surfaces

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### Mordell-Weil group of an abelian variety on the perfect closure of a finitely generated field

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### A functor on Abelian varieties corresponding to this operation on Weil numbers

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### Rigidity of universal abelian variety

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### Intersection of a certain linear ideals of $K[[X_1,\ldots,X_{np}]]$ for ${\mathrm{ch}}(K) = p > 0$

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### Application of Stein factorisation: rigidity lemma

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### Abelian varieties by Moonen and van der Geer: proof of rigidity lemma

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### Conditions for $p$-divisible group to come from an abelian variety

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### Isogeny components of Jacobians of étale covers

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### Standard application of Oort-Tate classification theorem

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### abelian variety with all over non degenerate pairing

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### The Weil restriction of an elliptic curve with respect to $\mathbb{F}_{p^2}/\mathbb{F}_{p}$

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### Is there a way to find any $\mathbb{F}_2(t)$-point on the elliptic curve $\mathcal{E}$?

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### What is the geometric quotient of the abelian threefold?

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