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Results tagged with abelian-varieties
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user 52824
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
Accepted
On a proposition in Hartshorne's paper "Ample vector bundles on curves"
The assertion (X) is false in any characteristic $p > 0$ for any $Y$ with genus at least 2. (It is true and easy for $Y$ of genus 1, and true and easy and uninteresting for $Y$ of genus 0.)
To see …
- 1,285
6
votes
Accepted
Why is the Tate local duality pairing compatible with the Cartier duality pairing?
To avoid notational confusion between translation in the derived category (of abelian fppf sheaves on the category of lfp $S$-schemes) and torsion in abelian schemes, I'll denote the $n$-torsion in $A …
- 1,285
5
votes
Accepted
Why is the norm map dual to restriction under Tate local duality?
Note first of all that the "norm" map you speak of does not make sense unless the field extension is separable. That is, for a separable field extension $k'/k$ of finite degree and a commutative $k$- …
- 1,285
4
votes
Accepted
kernel of isogeny becomes constant after base change
Do you really mean to consider an abelian scheme over the entire ring of integers, and not just a localization thereof? Either way, every finite flat group scheme $G$ over a domain $R$ with fraction …
- 1,285