Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local-global compatibility for regular algebraic cuspidal automorphic
  representation when $\ell \neq p$   We prove the compatibility of local and global Langlands correspondences for
$GL_n$ up to semisimplification for the Galois representations constructed by
Harris-Lan-Taylor-Thorne and Scholze. More precisely, let $r_p(\pi)$ denote an
$n$-dimensional $p$-adic representation of the Galois group of a CM field $F$
attached to a regular algebraic cuspidal automorphic representation $\pi$ of
$GL_n(\mathbb{A}_F)$. We show that the restriction of $r_p(\pi)$ to the
decomposition group of a place $v\nmid p$ of $F$ corresponds up to
semisimplification to $rec(\pi_v)$, the image of $\pi_v$ under the local
Langlands correspondence. Furthermore, we can show that the monodromy of the
associated Weil-Deligne representation of $.r_p(\pi)|_{G_{F_v}}$ is `more
nilpotent' than the monodromy of $rec(\pi_v)$.

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: physics