Geodesic
CATEGORIFYING RATIONALIZATION
Forum of Mathematics, Sigma, Tome 7 (2019)

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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, $K_{n}(S^{-1}E)\cong S^{-1}K_{n}(E)$. 
@article{10_1017_fms_2019_26,
     author = {CLARK BARWICK and SAUL GLASMAN and MARC HOYOIS and DENIS NARDIN and JAY SHAH},
     title = {CATEGORIFYING {RATIONALIZATION}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {7},
     year = {2019},
     doi = {10.1017/fms.2019.26},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.26/}
}
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CLARK BARWICK; SAUL GLASMAN; MARC HOYOIS; DENIS NARDIN; JAY SHAH. CATEGORIFYING RATIONALIZATION. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.26

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