CATEGORIFYING RATIONALIZATION
Autor: | CLARK BARWICK, SAUL GLASMAN, MARC HOYOIS, DENIS NARDIN, JAY SHAH |
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Jazyk: | angličtina |
Rok vydání: | 2019 |
Předmět: | |
Zdroj: | Forum of Mathematics, Sigma, Vol 7 (2019) |
Druh dokumentu: | article |
ISSN: | 2050-5094 |
DOI: | 10.1017/fms.2019.26 |
Popis: | 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, $K_{n}(S^{-1}E)\cong S^{-1}K_{n}(E)$. |
Databáze: | Directory of Open Access Journals |
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