Spherical DG-functors
Rina Anno
University of Pittsburgh, USATimothy Logvinenko
Cardiff University, UK
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Abstract
For two DG-categories A and B we define the notion of a spherical Morita quasi-functor . We construct its associated autoequivalences: the twist and the cotwist . 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.
Cite this article
Rina Anno, Timothy Logvinenko, Spherical DG-functors. J. Eur. Math. Soc. 19 (2017), no. 9, pp. 2577–2656
DOI 10.4171/JEMS/724