Algebraic K-theory of quotient stacks

2015/09/17 by Amalendu Krishna, Krishna, Amalendu, Charanya Ravi +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1509.05147

21 pages, Title changed, Final version, to appear in Annals of K-Theory

arxiv created 2017/08/02 · arxiv updated 2017/08/03

Abstract

We prove some fundamental results like localization, excision, Nisnevich descent and the Mayer-Vietoris property for equivariant regular blow-up for the equivariant K-theory of schemes with an affine group scheme action. We also show that the equivariant K-theory with finite coefficients is invariant under equivariant vector bundle morphisms. We show that the equivariant homotopy K-theory is invariant under equivariant vector bundle morphisms and satisfies all the above properties, including nil-invariance.

Cited by

• Equivariant localizing invariants of simple varieties

Related

• Equivariant Algebraic K-Theory and Derived completions II: the case of Equivariant Homotopy K-Theory and Equivariant K-Theory
• Equivariant Algebraic K-Theories
• The geometric K-theory of quotient stacks
• Thomason's completion for K-theory and cyclic homology of quotient stacks
• Equivariant Motivic Homotopy Theory