Noncommutative rigidity
In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of separably closed fields. As a byproduct, we obtain an extens...
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Springer Berlin Heidelberg
2018
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| Mynediad Ar-lein: | http://hdl.handle.net/1721.1/117123 https://orcid.org/0000-0001-5558-9236 |
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| 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 | In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of separably closed fields. As a byproduct, we obtain an extension of Suslin’s rigidity theorem, as well as of Yagunov-Østvær’s equivariant rigidity theorem, to singular varieties. Among other applications, we show that base-change along primary field extensions yields a faithfully flat morphism between noncommutative motivic Galois groups. Finally, along the way, we introduce the category of n-adic noncommutative mixed motives. Keywords: Algebraic cycles, K-theory, noncommutative algebraic geometry |
| first_indexed | 2024-09-23T12:43:08Z |
| format | Article |
| id | mit-1721.1/117123 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:43:08Z |
| publishDate | 2018 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1171232022-10-01T10:42:48Z Noncommutative rigidity Trigo Neri Tabuada, Goncalo Jorge Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of separably closed fields. As a byproduct, we obtain an extension of Suslin’s rigidity theorem, as well as of Yagunov-Østvær’s equivariant rigidity theorem, to singular varieties. Among other applications, we show that base-change along primary field extensions yields a faithfully flat morphism between noncommutative motivic Galois groups. Finally, along the way, we introduce the category of n-adic noncommutative mixed motives. Keywords: Algebraic cycles, K-theory, noncommutative algebraic geometry National Science Foundation (U.S.) (CAREER Award 1350472) Portuguese Science and Technology Foundation (Grant PEst-OE/MAT/UI0297/2014) 2018-07-25T18:06:52Z 2018-09-02T05:00:05Z 2017-11 2018-07-20T03:58:23Z Article http://purl.org/eprint/type/JournalArticle 0025-5874 1432-1823 http://hdl.handle.net/1721.1/117123 Tabuada, Gonçalo. “Noncommutative Rigidity.” Mathematische Zeitschrift, vol. 289, no. 3–4, Aug. 2018, pp. 1281–98. https://orcid.org/0000-0001-5558-9236 en https://doi.org/10.1007/s00209-017-1998-5 Mathematische Zeitschrift Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Trigo Neri Tabuada, Goncalo Jorge Noncommutative rigidity |
| title | Noncommutative rigidity |
| title_full | Noncommutative rigidity |
| title_fullStr | Noncommutative rigidity |
| title_full_unstemmed | Noncommutative rigidity |
| title_short | Noncommutative rigidity |
| title_sort | noncommutative rigidity |
| url | http://hdl.handle.net/1721.1/117123 https://orcid.org/0000-0001-5558-9236 |
| work_keys_str_mv | AT trigoneritabuadagoncalojorge noncommutativerigidity |