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Hecke operators for curves over non-archimedean local fields and related finite rings (2305.09595v3)
Published 16 May 2023 in math.NT, math.AG, and math.RT
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.