Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Local Langlands correspondence for $\GL_n$ over $p$-adic fields   We reprove the Local Langlands Correspondence for $\GL_n$ over $p$-adic
fields as well as the existence of $\ell$-adic Galois representations attached
to (most) regular algebraic conjugate self-dual cuspidal automorphic
representations, for which we prove a local-global compatibility statement as
in the book of Harris-Taylor.
  In contrast to the proofs of the Local Langlands Correspondence given by
Henniart and Harris-Taylor our proof completely by-passes the numerical Local
Langlands Correspondence of Henniart. Instead, we make use of a previous result
describing the inertia-invariant nearby cycles in certain regular situations.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: stat