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arXiv · 1511.05501

Equivariant noncommutative motives

Goncalo Tabuada
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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, equivariant algebraic K-theory, orbifold cohomology theory, etc. Among other results, we relate our theory with its commutative counterpart as well as with Panin's motivic 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 (different from 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 group of G-equivariant noncommutative Chow motives.

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Goncalo Tabuada. 2016-08-23. Equivariant noncommutative motives. https://arxiv.org/abs/1511.05501

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