Year: 2024
Type: article
Abstract: Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p≥0, and let N be its nilpotent cone. Under mild hypotheses, we construct for each nilpotent G-orbit C and each indecomposable tilting vector bundle T on C a certain complex S(C,T)∈DbCohG×Gm(N). We prove that these objects are (up to shift) precisely the indecomposable objects in the coheart of a certain co-t-structure. We then show that if p is larger than the Coxeter number, then the hypercohomology H∙(N,S(C,T)) is identified with the cohomology of a tilting module for G. This confirms a conjecture of Humphreys on the support of the cohomology of tilting modules.
Source: Duke Mathematical Journal
Authors: Pramod N. Achar, William Hardesty
Institutions: Louisiana State University, The University of Sydney
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3167102142