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Spherical DG-functors

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

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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

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