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Creators/Authors contains: "Kazhdan, David"

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  1. 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. 
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    Free, publicly-accessible full text available April 1, 2026
  2. Abstract: We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle. 
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