Equivariant algebraic K-theory

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In mathematics, the equivariant algebraic K-theory is an algebraic K-theory associated to the category of equivariant coherent sheaves on an algebraic scheme X with action of a linear algebraic group G, via Quillen's Q-construction; thus, by definition,

In particular, is the Grothendieck group of . The theory was developed by R. W. Thomason in 1980s.[1] Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem.

Equivalently, may be defined as the of the category of coherent sheaves on the quotient stack .[2][3] (Hence, the equivariant K-theory is a specific case of the K-theory of a stack.)

A version of the Lefschetz fixed-point theorem holds in the setting of equivariant (algebraic) K-theory.[4]