Spherical DG-functors

Anno, Rina and Logvinenko, Timothy ORCID: https://orcid.org/0000-0001-5279-6977 2017. Spherical DG-functors. Journal of the European Mathematical Society 19 (9) , pp. 2577-2656. 10.4171/JEMS/724

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Abstract

For two DG-categories A and B we define the notion of a spherical Morita quasi-functor A → B. We construct its associated autoequivalences: the twist T ∈ Aut D(B) and the co-twist F ∈ Aut D(A). We give sufficiency criteria for a quasi-functor to be spherical and for the twists associated to a collection of spherical quasi-functors to braid. Using the framework of DG-enhanced triangulated categories, we translate all of the above to Fourier-Mukai transforms between the derived categories of algebraic varieties. This is a broad generalisation of the results on spherical objects in [ST01] and on spherical functors in [Ann07]. In fact, this paper replaces [Ann07], which has a fatal gap in the proof of its main theorem. Though conceptually correct, the proof was impossible to fix within the framework of triangulated categories.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	European Mathematical Society
ISSN:	1435-9855
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	15 February 2016
Last Modified:	31 Oct 2022 11:00
URI:	https://orca.cardiff.ac.uk/id/eprint/87061

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