Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology with integral coefficients of stacks of shtukas   We construct the cuspidal cohomology groups of stacks of shtukas with
$\mathbb Z_{\ell}$-coefficients and prove that they are $\mathbb
Z_{\ell}$-modules of finite type. We prove that the cohomology groups with
compact support of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients are
modules of finite type over a Hecke algebra with $\mathbb
Z_{\ell}$-coefficients.
  As an application, we prove that the cuspidal cohomology groups with $\mathbb
Q_{\ell}$-coefficients are equal to the Hecke-finite cohomology groups with
$\mathbb Q_{\ell}$-coefficients defined by V. Lafforgue.

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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: physics
20
The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph