Abstract
We solve a problem proposed by Khovanov by constructing, for any set of primes S, a triangulated category (in fact a stable ∞-category) whose Grothendieck group is S−1Z. More generally, for any exact ∞-category E, we construct an exact ∞-category S−1E of equivariant sheaves on the Cantor space with respect to an action of a dense subgroup of the circle. We show that this ∞-category is precisely the result of categorifying division by the primes in S. In particular, Kn(S−1E) ∼= S−1 Kn(E).
Original language | English |
---|---|
Article number | e42 |
Number of pages | 15 |
Journal | Forum of Mathematics, Sigma |
Volume | 7 |
DOIs | |
Publication status | Published - 9 Jan 2020 |
Fingerprint
Dive into the research topics of 'Categorifying rationalization'. Together they form a unique fingerprint.Profiles
-
Clark Barwick
- School of Mathematics - Personal Chair of Pure Mathematics
Person: Academic: Research Active (Teaching)