Equivariant noncommutative motives
Name
1511.05501.pdf
Size
461.61 KB
Format
Adobe PDF
Checksum (MD5)
4d0b026bbf2e4148a435d7e3ee598e6e
Author(s)
Trigo Neri Tabuada, Goncalo Jorge
Date Issued
January 2018
Journal
Annals of K-Theory
Publisher
Mathematical Sciences Publishers
Citation
Tabuada, Gonçalo. “Equivariant Noncommutative Motives.” Annals of K-Theory 3, 1 (January 2018): 125–156 © 2018 Mathematical Sciences Publishers
Version
Original manuscript
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.
Keywords: G-scheme; 2-cocycle; semidirect product algebra; twisted group algebra; equivariant algebraic K-theory; twisted projective homogeneous scheme; full exceptional collection; equivariant motivic measure; noncommutative algebraic geometry
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2140/AKT.2018.3.125
