Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattices in Tate modules   Refining a theorem of Zarhin, we prove that given a $g$-dimensional abelian
variety $X$ and an endomorphism $u$ of $X$, there exists a matrix $A \in
\operatorname{M}_{2g}(\mathbb{Z})$ such that each Tate module $T_\ell X$ has a
$\mathbb{Z}_\ell$-basis on which the action of $u$ is given by $A$.

0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph