TY - JOUR
T1 - Hecke Operators for Curves Over Non-Archimedean Local Fields and Related Finite Rings
AU - Braverman, Alexander
AU - Kazhdan, David
AU - Polishchuk, Alexander
AU - Fai Wong, Ka
N1 - Publisher Copyright:
© The Author(s) 2025. Published by Oxford University Press. All rights reserved.
PY - 2025/4/1
Y1 - 2025/4/1
N2 - We study Hecke operators associated with curves over a non-archimedean local field K and over the rings O/mN, where O ⊂ K is the ring of integers. Our main result is commutativity of a certain “small” local Hecke algebra over O/mN, 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.
AB - We study Hecke operators associated with curves over a non-archimedean local field K and over the rings O/mN, where O ⊂ K is the ring of integers. Our main result is commutativity of a certain “small” local Hecke algebra over O/mN, 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.
UR - http://www.scopus.com/inward/record.url?scp=105003042644&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnaf075
DO - 10.1093/imrn/rnaf075
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AN - SCOPUS:105003042644
SN - 1073-7928
VL - 2025
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 7
M1 - rnaf075
ER -