Relative assembly maps and the K-theory of Hecke algebras in prime characteristic
Year: 2024
Type: article
Abstract: We investigate the relative assembly map from the family of finite subgroups to the family of virtually cyclic subgroups for the algebraic K-theory of twisted group rings of a group G with coefficients in a regular ring R or, more generally, with coefficients in a regular additive category. They are known to be isomorphisms rationally. We show that it suffices to invert only those primes p for which G contains a non-trivial finite p-group and p is not invertible in R. The key ingredient is the detection of Nil-terms of a twisted group ring of a finite group F after localizing at p in terms of the p-subgroups of F using Verschiebungs and Frobenius operators. We construct and exploit the structure of a module over the ring of big Witt vectors on the Nil-terms. We analyze the algebraic K-theory of the Hecke algebras of subgroups of reductive p-adic groups in prime characteristic.
Source: Mathematische Annalen
Author: W. Lück
Institution: University of Bonn
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4401820165