CATEGORIFYING RATIONALIZATION
We construct, for any set of primes $S$, a triangulated category (in fact a stable $\infty$-category) whose Grothendieck group is $S^{-1}\mathbf{Z}$. More generally, for any exact $\infty$-category $E$, we construct an exact $\infty$-category $S^{-1}E$ of equivariant sheaves on the Cantor space with...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2019-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509419000264/type/journal_article |
| _version_ | 1811156202138107904 |
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| author | CLARK BARWICK SAUL GLASMAN MARC HOYOIS DENIS NARDIN JAY SHAH |
| author_facet | CLARK BARWICK SAUL GLASMAN MARC HOYOIS DENIS NARDIN JAY SHAH |
| author_sort | CLARK BARWICK |
| collection | DOAJ |
| description | We construct, for any set of primes $S$, a triangulated category (in fact a stable $\infty$-category) whose Grothendieck group is $S^{-1}\mathbf{Z}$. More generally, for any exact $\infty$-category $E$, we construct an exact $\infty$-category $S^{-1}E$ of equivariant sheaves on the Cantor space with respect to an action of a dense subgroup of the circle. We show that this $\infty$-category is precisely the result of categorifying division by the primes in $S$. In particular, $K_{n}(S^{-1}E)\cong S^{-1}K_{n}(E)$. |
| first_indexed | 2024-04-10T04:47:33Z |
| format | Article |
| id | doaj.art-cc111a5a43e64d94adcaa3ae98012985 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:33Z |
| publishDate | 2019-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-cc111a5a43e64d94adcaa3ae980129852023-03-09T12:34:44ZengCambridge University PressForum of Mathematics, Sigma2050-50942019-01-01710.1017/fms.2019.26CATEGORIFYING RATIONALIZATIONCLARK BARWICK0SAUL GLASMANMARC HOYOIS1DENIS NARDIN2JAY SHAH3School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK;Department of Mathematics, University of Southern California, 3620 South Vermont Avenue, Los Angeles, CA 90089, USA;Département de Mathématiques, Institut Galilée, Université Paris 13, 99 av. J.B. Clément, 93430 Villetaneuse, France;Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, IN 46556, USA;We construct, for any set of primes $S$, a triangulated category (in fact a stable $\infty$-category) whose Grothendieck group is $S^{-1}\mathbf{Z}$. More generally, for any exact $\infty$-category $E$, we construct an exact $\infty$-category $S^{-1}E$ of equivariant sheaves on the Cantor space with respect to an action of a dense subgroup of the circle. We show that this $\infty$-category is precisely the result of categorifying division by the primes in $S$. In particular, $K_{n}(S^{-1}E)\cong S^{-1}K_{n}(E)$.https://www.cambridge.org/core/product/identifier/S2050509419000264/type/journal_article19D99 (primary)18F25 (secondary) |
| spellingShingle | CLARK BARWICK SAUL GLASMAN MARC HOYOIS DENIS NARDIN JAY SHAH CATEGORIFYING RATIONALIZATION Forum of Mathematics, Sigma 19D99 (primary) 18F25 (secondary) |
| title | CATEGORIFYING RATIONALIZATION |
| title_full | CATEGORIFYING RATIONALIZATION |
| title_fullStr | CATEGORIFYING RATIONALIZATION |
| title_full_unstemmed | CATEGORIFYING RATIONALIZATION |
| title_short | CATEGORIFYING RATIONALIZATION |
| title_sort | categorifying rationalization |
| topic | 19D99 (primary) 18F25 (secondary) |
| url | https://www.cambridge.org/core/product/identifier/S2050509419000264/type/journal_article |
| work_keys_str_mv | AT clarkbarwick categorifyingrationalization AT saulglasman categorifyingrationalization AT marchoyois categorifyingrationalization AT denisnardin categorifyingrationalization AT jayshah categorifyingrationalization |