All Questions

Do there exist uncountably many abelian surfaces with good reduction over $\mathbb{Q}_p$ with pairwise non-isomorphic rational $p$-adic Tate modules? If we took $l$-adic Tate modules there would be ...

Where do I find a proof of the fact that over global function fields of characteristic $p>0$, finiteness of the Tate-Shafarevich group of an abelian variety is equivalent to finiteness of its $\ell$...

The etale cohomolgoy of a variety $X$ over a number field $K$ is a Galois representation of $\mathrm{Gal}(\overline K/K)$ with some properties coming from $X$, e.g., it is unramified outside $S$ if $X$...

Let $A$ be an abelian variety over a field $k$ of dimension $g$, and $H$ be a Weil cohomology theory for smooth projective varieties over $k$ with characteristic $0$ coefficient field $E$. Is it ...

Quadratic twists of elliptic curves (or, more generally, abelian varieties) are familiar objects in arithmetic geometry. I would like to extend that definition to the category of 1-motives over global ...

This question is somewhat inspired by Kevin Buzzard's answer to What is the interpretation of complex multiplication in terms of Langlands? and somewhat from my own curiosity about such topics. Let $...