Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: P-adic L-functions for GL(3)   Let $\Pi$ be a regular algebraic cuspidal automorphic representation of
$\mathrm{GL}_3(\mathbb{A}_{\mathbb{Q}})$. When $\Pi$ is $p$-ordinary for the
maximal standard parabolic with Levi $\mathrm{GL}_1 \times \mathrm{GL}_2$, we
construct a $p$-adic $L$-function for $\Pi$. More precisely, we construct a
(single) bounded measure $L_p(\Pi)$ on $\mathbb{Z}_p^\times$ attached to $\Pi$,
and show it interpolates all the critical values $L(\Pi\times\eta,-j)$ at $p$
in the left-half of the critical strip for $\Pi$ (for varying $\eta$ and $j$).
This proves conjectures of Coates--Perrin-Riou and Panchishkin in this case.
Our construction uses the theory of spherical varieties to build a "Betti Euler
system'', a norm-compatible system of classes in the Betti cohomology of a
locally symmetric space for $\mathrm{GL}_3$. We work in arbitrary cohomological
weight, allow arbitrary ramification at $p$ along the other maximal standard
parabolic, and make no self-duality assumption.

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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-alg