Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived deformation rings allowing congruences]{Derived deformation
  rings allowing congruences   We generalize a result of Galatius and Venkatesh which relates the graded
module of cohomology of locally symmetric spaces to the graded homotopy ring of
the derived Galois deformation rings, by removing certain assumptions, and in
particular by allowing congruences inside the localized Hecke algebra.

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The categories of this paper are: quant-ph
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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: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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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: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph