Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lefschetz number formula for Shimura varieties of Hodge type   For any Shimura variety of Hodge type with hyperspecial level at a prime $p$
and automorphic lisse sheaf on it, we prove a formula, conjectured by Kottwitz
\cite{Kottwitz90}, for the Lefschetz numbers of Frobenius-twisted Hecke
correspondences acting on the compactly supported \'etale cohomology. Our proof
is an adaptation of the arguments of Langlands and Rapoport \cite{LR87} of
deriving the Kottwitz's formula from their conjectural description of the set
of mod-$p$ points of Shimura variety (Langlands-Rapoport conjecture), which
replaces their Galois gerb theoretic arguments by more geometric ones. We also
prove a generalization of Honda-Tate theorem in the context of Shimura
varieties and fix an error in Kisin's work \cite{Kisin17}. We do not assume
that the derived group is simply connected.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: econ