Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A finiteness theorem for Galois representations of function fields over
  finite fields (after Deligne)   Revised: just some typos, reorganized a bit the article. It will be published
in the VIASM Annual meeting, Hanoi.
  We give a detailed account of Deligne's letter to Drinfeld dated June 18,
2011, in which he shows that there are finitely many irreducible lisse $\bar
\Q_\ell$-sheaves with bounded ramification, up to isomorphism and up to twist,
on a smooth variety defined over a finite field. The proof relies on
Lafforgue's Langlands correspondence over curves. In addition, Deligne shows
the existence of affine moduli of finite type over $\mathbb{Q}$. A corollary of
Deligne's finiteness theorem is the existence of a number field which contains
all traces of the Frobenii at closed points, which was the main result of his
recent article and which answers positively his own conjecture from Weil II.

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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat