Equivariant algebraic K-theory

In mathematics, the equivariant algebraic K-theory is an algebraic K-theory associated to the category Coh G ⁡ ( X ) {\displaystyle \operatorname {Coh} ^{G}(X)} 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, K i G ( X ) = π i ( B + Coh G ⁡ ( X ) ) . {\displaystyle K_{i}^{G}(X)=\pi _{i}(B^{+}\operatorname {Coh} ^{G}(X)).} In particular, K 0 G ( C ) {\displaystyle K_{0}^{G}(C)} is the Grothendieck group of Coh G ⁡ ( X ) {\displaystyle \operatorname {Coh} ^{G}(X)} .

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