TY  - JOUR
ID  - city27129
EP  - 164
AV  - restricted
N1  - © 2021 Joseph Chuang and Andrey Lazarev, published by De Gruyter. This work is licensed
under the Creative Commons Attribution 4.0 International License.
JF  - Journal für die reine und angewandte Mathematik
A1  - Chuang, J.
A1  - Lazarev, A.
SP  - 127
UR  - https://doi.org/10.1515/crelle-2021-0052
IS  - 781
Y1  - 2021/12/01/
TI  - Rank functions on triangulated categories
PB  - Walter de Gruyter GmbH
VL  - 2021
SN  - 0075-4102
N2  - We introduce the notion of a rank function on a triangulated category C which generalizes the Sylvester rank function in the case when C D Perf.A/ is the perfect derived category of a ring A. We show that rank functions are closely related to functors into simple triangulated categories and classify Verdier quotients into simple triangulated categories in terms of particular rank functions called localizing. If C D Perf.A/ as above, localizing rank functions also classify finite homological epimorphisms from A into differential graded skew-fields or, more generally, differential graded Artinian rings. To establish these results, we develop the theory of derived localization of differential graded algebras at thick subcategories of their perfect derived categories. This is a far-reaching generalization of Cohn?s matrix localization of rings and has independent interest.
ER  -