Notes on G-theory of Deligne-Mumford stacks
B. Toen
TL;DR
This paper explores the rational G-theory of Deligne-Mumford stacks, extending Riemann-Roch methods to define new filtrations and study equivariant K-theory over general bases.
Contribution
It provides a description of the rational G-theory of Deligne-Mumford stacks and introduces new filtrations on K-theory, expanding the theoretical framework.
Findings
Description of rational G-theory for Deligne-Mumford stacks
Development of new filtrations on K-theory
Applications to equivariant K-theory
Abstract
Based on the methods used by the author to prove the Riemann-Roch formula for algebraic stacks, this paper contains a description of the rationnal G-theory of Deligne-Mumford stacks over general bases. We will use these results to study equivariant K-theory, and also to define new filtrations on K-theory of algebraic stacks.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models