Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independence of $\ell$ for Frobenius conjugacy classes attached to
  abelian varieties   Let $A$ be an abelian variety over a number field $\mathrm E\subset \mathbb
C$ and let $\mathbf G$ denote the Mumford--Tate group of $A$. After replacing
$\mathrm E$ by a finite extension, the action of the absolute Galois group
$\mathrm{Gal}(\overline{\mathrm E}/\mathrm E)$ on the $\ell$-adic cohomology
$\mathrm{H}^1_{\mathrm{\acute{e}t}}(A_{\overline{\mathrm E}},\mathbb Q_\ell)$
factors through $\mathbf G(\mathbb Q_\ell).$ We show that for $v$ an odd prime
of $\mathrm E$ where $A$ has good reduction, the conjugacy class of Frobenius
$\mathrm{Frob}_v$ in $\mathbf G(\mathbb Q_\ell)$ is independent of $\ell$.
Along the way we prove that every point in the $\mu$-ordinary locus of the
special fiber of Shimura varieties has a special point lifting it.

34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th