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arXiv · 2305.09595

Hecke operators for curves over non-archimedean local fields and related finite rings

Alexander Braverman·David Kazhdan·Alexander Polishchuk·Ka Fai Wong
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Abstract

We study Hecke operators associated with curves over a non-archimedean local field $K$ and over the rings $O/{\mathfrak m}^N$, where $O\subset K$ is the ring of integers. Our main result is commutativity of a certain "small" local Hecke algebra over $O/{\mathfrak m}^N$, associated with a connected split reductive group $G$ such that $[G,G]$ is simple and simpy connected. The proof uses a Hecke algebra associated with $G(K(\!(t)\!))$ and a global argument involving $G$-bundles on curves.

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Alexander Braverman, David Kazhdan, Alexander Polishchuk, Ka Fai Wong. 2023-05-16. Hecke operators for curves over non-archimedean local fields and related finite rings. https://arxiv.org/abs/2305.09595

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