Equivariant noncommutative motives
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 c...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Published: |
Mathematical Sciences Publishers
2018
|
| Online Access: | http://hdl.handle.net/1721.1/116064 https://orcid.org/0000-0001-5558-9236 |
| _version_ | 1811074157491781632 |
|---|---|
| author | Trigo Neri Tabuada, Goncalo Jorge |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge |
| author_sort | Trigo Neri Tabuada, Goncalo Jorge |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T09:44:21Z |
| format | Article |
| id | mit-1721.1/116064 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:44:21Z |
| publishDate | 2018 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | mit-1721.1/1160642022-09-30T16:32:07Z Equivariant noncommutative motives Trigo Neri Tabuada, Goncalo Jorge Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge 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 National Science Foundation (U.S.) (Award 1350472) 2018-06-04T18:22:41Z 2018-06-04T18:22:41Z 2018-01 2017-04 2018-05-31T15:40:07Z Article http://purl.org/eprint/type/JournalArticle 2379-1691 2379-1683 http://hdl.handle.net/1721.1/116064 Tabuada, Gonçalo. “Equivariant Noncommutative Motives.” Annals of K-Theory 3, 1 (January 2018): 125–156 © 2018 Mathematical Sciences Publishers https://orcid.org/0000-0001-5558-9236 http://dx.doi.org/10.2140/AKT.2018.3.125 Annals of K-Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Mathematical Sciences Publishers arXiv |
| spellingShingle | Trigo Neri Tabuada, Goncalo Jorge Equivariant noncommutative motives |
| title | Equivariant noncommutative motives |
| title_full | Equivariant noncommutative motives |
| title_fullStr | Equivariant noncommutative motives |
| title_full_unstemmed | Equivariant noncommutative motives |
| title_short | Equivariant noncommutative motives |
| title_sort | equivariant noncommutative motives |
| url | http://hdl.handle.net/1721.1/116064 https://orcid.org/0000-0001-5558-9236 |
| work_keys_str_mv | AT trigoneritabuadagoncalojorge equivariantnoncommutativemotives |