HOMOLOGICAL STRATIFICATION AND DESCENT
Abstract
Abstract We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits excellent descent properties. In conjunction with Balmer’s Nerves of Steel conjecture, we conclude that classical stratification also admits a general form of descent. This gives a uniform treatment of several recent stratification results and provides a complete answer to the question: When does stratification descend? As a new application, we extend earlier work on the tensor triangular geometry of equivariant module spectra from finite groups to compact Lie groups.
Fields of Study & Subjects
History and Theory of Mathematics
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 2
- Pages
- 1081–1125
- Publication date
- 29 January 2026
- Language
- EN