Year: 2025
Type: article
Abstract: YAYLALIWe use the construction of the stable homotopy category by Khan and Ravi to calculate the integral T-equivariant K-theory spectrum of a flag variety over an affine scheme, where T is a split torus associated to the flag variety.More precisely, we show that the T-equivariant K-theory ring spectrum of a flag variety is decomposed into a direct sum of K-theory spectra of the classifying stack BT indexed by the associated Weyl group.We also explain how to relate these results to the motivic world and deduce classical results for T-equivariant intersection theory and K-theory of flag varieties.For this purpose, we analyze the motive of schemes stratified by affine spaces with group action, that preserves these stratifications.We work with cohomology theories, that satisfy certain vanishing conditions, which are satisfied for example by motivic cohomology and K-theory.
Source: Algebraic & Geometric Topology
Author: Can Yaylali
Institution: Technische Universität Darmstadt
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4413378759