On Atiyah-Segal completion for Hermitian K-theory / von Herman Rohrbach. Wuppertal, September 2021
Inhalt
- Introduction
- Preliminaries
- Classifying spaces
- Linear algebraic groups
- Representation theory of linear algebraic groups
- Torsors in sites
- Free actions in the category of schemes
- Nisnevich and étale classifying spaces
- Geometric classifying spaces
- Milnor exact sequence
- Semi-orthogonal decompositions
- dg Modules over a commutative ring
- dg Categories
- dg Modules over a dg category
- Exact and pretriangulated dg categories
- Localization of dg categories
- Semi-orthogonal decompositions of dg categories
- Grothendieck-Witt theory
- Grothendieck-Witt groups of categories with duality
- Fundamental results
- Equivariant Grothendieck-Witt theory
- Projective bundle formula
- Duality on the dg category of perfect complexes
- Constructing symmetric forms from Koszul complexes
- Cutting the Koszul complex in half abstractly
- Grothendieck-Witt spectra of projective bundles
- Atiyah-Segal completion for split tori
- Connected split reductive groups
- Grothendieck-Witt spectra of Grassmannians
- Semi-orthogonal decompositions for Grassmannians
- Duality on Young diagrams
- The Grothendieck-Witt spectrum of an even Grassmannian
- The Grothendieck-Witt theory of the classifying space of a general linear group
- Appendix