E[subscript n]-Regularity Implies E[subscript n-1]-Regularity
Vorst and Dayton-Weibel proved that K[subscript n]-regularity implies K[subscript n−1]-regularity. In this article we generalize this result from (commutative) rings to differential graded categories and from algebraic K-theory to any functor which is Morita invariant, continuous, and localizing. Mo...
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| Format: | Article |
| Language: | en_US |
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European Math Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/93241 https://orcid.org/0000-0001-5558-9236 |
| _version_ | 1826190334097358848 |
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| author | Trigo Neri Tabuada, Goncalo Jo |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jo |
| author_sort | Trigo Neri Tabuada, Goncalo Jo |
| collection | MIT |
| description | Vorst and Dayton-Weibel proved that K[subscript n]-regularity implies K[subscript n−1]-regularity. In this article we generalize this result from (commutative) rings to differential graded categories and from algebraic K-theory to any functor which is Morita invariant, continuous, and localizing. Moreover, we show that regularity is preserved under taking desuspensions, fibers of morphisms, direct factors, and arbitrary direct sums. As an application, we prove that the above implication also holds for schemes. Along the way, we extend Bass’ fundamental theorem to this broader setting and establish a Nisnevich descent result which is of independent interest. |
| first_indexed | 2024-09-23T08:38:41Z |
| format | Article |
| id | mit-1721.1/93241 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:38:41Z |
| publishDate | 2015 |
| publisher | European Math Society |
| record_format | dspace |
| spelling | mit-1721.1/932412022-09-30T10:11:06Z E[subscript n]-Regularity Implies E[subscript n-1]-Regularity Trigo Neri Tabuada, Goncalo Jo Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jo Vorst and Dayton-Weibel proved that K[subscript n]-regularity implies K[subscript n−1]-regularity. In this article we generalize this result from (commutative) rings to differential graded categories and from algebraic K-theory to any functor which is Morita invariant, continuous, and localizing. Moreover, we show that regularity is preserved under taking desuspensions, fibers of morphisms, direct factors, and arbitrary direct sums. As an application, we prove that the above implication also holds for schemes. Along the way, we extend Bass’ fundamental theorem to this broader setting and establish a Nisnevich descent result which is of independent interest. NEC Corporation (Award) Portuguese Science and Technology Foundation (PEst-OE/MAT/UI0297/2011) 2015-01-30T19:31:54Z 2015-01-30T19:31:54Z 2014 2013-07 Article http://purl.org/eprint/type/JournalArticle 1431-0635 1431-0643 http://hdl.handle.net/1721.1/93241 Tabuada, Goncalo. "E[subscript n]-Regularity Implies E[subscript n-1]-Regularity." Documenta Mathematica 19 (2014), 121-139. https://orcid.org/0000-0001-5558-9236 en_US http://www.math.uiuc.edu/documenta/vol-19/04.pdf Documenta Mathematica Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf European Math Society arXiv |
| spellingShingle | Trigo Neri Tabuada, Goncalo Jo E[subscript n]-Regularity Implies E[subscript n-1]-Regularity |
| title | E[subscript n]-Regularity Implies E[subscript n-1]-Regularity |
| title_full | E[subscript n]-Regularity Implies E[subscript n-1]-Regularity |
| title_fullStr | E[subscript n]-Regularity Implies E[subscript n-1]-Regularity |
| title_full_unstemmed | E[subscript n]-Regularity Implies E[subscript n-1]-Regularity |
| title_short | E[subscript n]-Regularity Implies E[subscript n-1]-Regularity |
| title_sort | e subscript n regularity implies e subscript n 1 regularity |
| url | http://hdl.handle.net/1721.1/93241 https://orcid.org/0000-0001-5558-9236 |
| work_keys_str_mv | AT trigoneritabuadagoncalojo esubscriptnregularityimpliesesubscriptn1regularity |