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2018 Equivariant noncommutative motives
Gonçalo Tabuada
Ann. K-Theory 3(1): 125-156 (2018). DOI: 10.2140/akt.2018.3.125

Abstract

Given a finite group G, we develop a theory of G-equivariant noncommutative motives. This theory provides a well-adapted framework for the study of G-schemes, Picard groups of schemes, G-algebras, 2-cocycles, G-equivariant algebraic K-theory, etc. Among other results, we relate our theory with its commutative counterpart as well as with Panin’s theory. As a first application, we extend Panin’s computations, concerning twisted projective homogeneous varieties, to a large class of invariants. As a second application, we prove that whenever the category of perfect complexes of a G-scheme X admits a full exceptional collection of G-invariant (G-equivariant) objects, the G-equivariant Chow motive of X is of Lefschetz type. Finally, we construct a G-equivariant motivic measure with values in the Grothendieck ring of G-equivariant noncommutative Chow motives.

Citation

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Gonçalo Tabuada. "Equivariant noncommutative motives." Ann. K-Theory 3 (1) 125 - 156, 2018. https://doi.org/10.2140/akt.2018.3.125

Information

Received: 23 August 2016; Revised: 5 April 2017; Accepted: 19 April 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 1374.14003
MathSciNet: MR3695366
Digital Object Identifier: 10.2140/akt.2018.3.125

Subjects:
Primary: 14A22 , 14L30 , 16S35 , 19L47 , 55N32

Keywords: $\mathrm G$-scheme , $2$-cocycle , equivariant algebraic $K\mkern-2mu$-theory , equivariant motivic measure , full exceptional collection , noncommutative algebraic geometry , semidirect product algebra , twisted group algebra , twisted projective homogeneous scheme

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.3 • No. 1 • 2018
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