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Results tagged with arithmetic-geometry
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user 26737
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
4
votes
Motivation for the Jacobian Variety
As outlined by the other answers, the Jacobian $J_X$ of a curve $X$ defined over $\mathbb{F}_q$ indeed encapsulates all cohomology information of $X$. In particular one can read the zeta function $\ze …
- 1,176
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