Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfectoid Shimura varieties and the Calegari-Emerton conjectures   We prove many new cases of a conjecture of Calegari-Emerton describing the
qualitative properties of completed cohomology. The heart of our argument is a
careful inductive analysis of completed cohomology on the Borel-Serre boundary.
As a key input to this induction, we prove a new perfectoidness result for
towers of minimally compactified Shimura varieties of pre-abelian type,
generalizing previous work of Scholze.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex