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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 simply connected. The proof uses a Hecke algebra associated with $$G(K(\!(t)\!))$$ and a global argument involving $$G$$-bundles on curves.more » « lessFree, publicly-accessible full text available April 1, 2026
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