Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally analytic completed cohomology of Shimura varieties and
  overconvergent $\mathrm{BGG}$ maps   We generalize the work of Lue Pan on locally analytic completed cohomology of
modular curves to Shimura varieties. In the process, we extend the axiomatic
Sen-Tate formalism of Berger-Colmez to a certain class of locally analytic
representations. Using Sen theory over rigid spaces, we define a geometric Sen
operator which is nothing but a pro\'etale Higgs bundle related with the
$p$-adic Simpson correspondence. In the application to Shimura varieties, we
obtain a proof of the rational Calegari-Emerton conjectures without a
perfectoid assumption at infinite level. We also construct the overconvergent
$\mathrm{BGG}$ maps for the derived Jacquet module of the locally analytic
completed cohomology and its dual.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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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: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph