Abstract
In this paper we give an example of a triangulated category, linear over a field of characteristic zero, which does not carry a DG-enhancement. The only previous examples of triangulated categories without a model have been constructed by Muro, Schwede and Strickland. These examples are however not linear over a field.
| Original language | English |
|---|---|
| Pages (from-to) | 393-437 |
| Number of pages | 45 |
| Journal | Annals of Mathematics |
| Volume | 191 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Mar 2020 |
Bibliographical note
Funding Information:Keywords: triangulated category, model, enhancement AMS Classification: Primary: 13D09, 18E30, 14A22. The first author is a Lecturer at the University of Liverpool. She is supported by EPSRC grant EP/N021649/1. The second author is a senior researcher at the Research Foundation -Flanders (FWO). He is supported by the FWO-grant G0D8616N “Hochschild cohomology and deformation theory of triangulated categories.” ©c 2020 Department of Mathematics, Princeton University. 1Notwithstanding what we say here, almost everything we do is valid in arbitrary characteristic. However in finite characteristic we would also have to consider topological enhancements, and we do not discuss these in the current paper. 2We can always transform an A∞-enhancement into a DG-enhancement by taking its DG-hull. See [7, p. 127] or [12, App. C].
Funding Information:
The first author is a Lecturer at the University of Liverpool. She is supported by EPSRC grant EP/N021649/1. The second author is a senior researcher at the Research Foundation - Flanders (FWO). He is supported by the FWO-grant G0D8616N \Hochschild cohomology and deformation theory of triangulated categories."
Publisher Copyright:
© 2020. Department of Mathematics, Princeton University.
Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.