Abstract
AbstractIn this paper, we prove homological stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category OrI(R) and prove a local Noetherianity theorem for the category of OrI(R)-modules. This implies an asymptotic structure theorem for orthogonal groups. In addition, we show general homological stability theorems for orthogonal groups, with both untwisted and twisted coefficients.
Funder
Directorate for Mathematical and Physical Sciences
Massachusetts Institute of Technology
Publisher
Springer Science and Business Media LLC
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