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Results tagged with abelian-varieties
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user 4790
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.
7
votes
The Poincare Bundle(s) on C \times J
The point is that $q_{2*}P(g-1)$ is a torsion-free sheaf, because it is the image of a torsion-free sheaf. Its support is concentrated on the Theta divisor; but this means that it is torsion, so it mu …
- 27k
20
votes
Accepted
isomorphism of abelian varieties
This is false even for elliptic curves over $\mathbb{C}$. This was proved by T. Shioda in "Some remarks on abelian varieties" J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), no. 1, 11-21, http:/ …
- 27k
3
votes
Weil restriction of abelian schemes along finite étale (resp. finite locally free) morphisms
Let $X \to S'$ be a smooth projective morphism, and $S' \to S$ a finite étale morphism.
The Weil restriction $Y \to S$ of $X \to S'$ is a closed subscheme of the scheme of morphisms $S' \to X$ on $S …
- 27k