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Results tagged with abelian-varieties
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user 26737
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.
8
votes
Defining isogenies over smaller fields
There is another obvious obstruction: by definition two twists are isomorphics above an extension, but are not isomorphic above their field of definition (and also not isogenous).
I believe that thes …
- 1,176
1
vote
Accepted
The size of endomorphism rings and the relation to ordinariness of Abelian surfaces
The general reference for this sort of questions is Waterhouse, Abelian varieties over finite fields. Your question is answered in: Theorem 7.2. If $A$ is ordinary (and simple), then $\mathop{End}(A)$ …
- 1,176