CATEGORIFYING RATIONALIZATION

Autor: CLARK BARWICK, SAUL GLASMAN, MARC HOYOIS, DENIS NARDIN, JAY SHAH
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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