Spherical DG-functors

By R. Anno, T. Logvinenko. 2013

125 citations recorded by the source corpus.

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 of D(B) and the co-twist F of D(A). We give powerful 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0b9767b9d5266a5f17455b54557ee608ddd3af50

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In Algebra and Number Theory

1. Christopher Brav
2. Tobias Dyckerhoff
3. Nick Sheridan

In Geometry and Topology

1. Christopher Brav
2. Tobias Dyckerhoff
3. P. Seidel
4. Nick Sheridan

In Mathematical Physics

1. Christopher Brav
2. Tobias Dyckerhoff
3. P. Seidel

Citations in the corpus

• Relative Calabi–Yau structures (2016, background): “10) admits a particularly nice interpretation if we assume the dg functor f to be spherical in the sense of [AL13] (this is satisfied in many of our examples): in this case, the B-bimodule cone(c) represents an autoequivalence of ModB known as a spherical twist of the adjunction.”