Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing the mod-$\ell$ local Langlands correspondence by
  nilpotent gamma factors   Let $F$ be a $p$-adic field and choose $k$ an algebraic closure of
$\mathbb{F}_{\ell}$, with $\ell$ different from $p$. We define ``nilpotent
lifts'' of irreducible generic $k$-representations of $GL_n(F)$, which take
coefficients in Artin local $k$-algebras. We show that an irreducible generic
$\ell$-modular representation $\pi$ of $GL_n(F)$ is uniquely determined by its
collection of Rankin--Selberg gamma factors $\gamma(\pi\times
\widetilde{\tau},X,\psi)$ as $\widetilde{\tau}$ varies over nilpotent lifts of
irreducible generic $k$-representations $\tau$ of $GL_t(F)$ for $t=1,\dots,
\lfloor \frac{n}{2}\rfloor$. This gives a characterization of the mod-$\ell$
local Langlands correspondence in terms of gamma factors, assuming it can be
extended to a surjective local Langlands correspondence on nilpotent lifts.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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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: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol