No CrossRef data available.
Article contents
CATEGORIFYING RATIONALIZATION
Published online by Cambridge University Press: 09 January 2020
Abstract
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,
$K_{n}(S^{-1}E)\cong S^{-1}K_{n}(E)$.
MSC classification
- Type
- Research Article
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s) 2019