Some finiteness results for Fourier-Mukai partners

Abstract

We develop some methods for studying the Fourier-Mukai partners of an algebraic variety. As applications we prove that abelian varieties have finitely many Fourier-Mukai partners and that they are uniquely determined by their derived category of coherent $D$-modules. We also generalize a famous theorem due to A. Bondal and D. Orlov.

17 pages, some concessions had to be made with regards to when the autoequivalence group produces an arithmetic action on cohomology

References in corpus (1)

• Triangulated categories of singularities and D-branes in Landau-Ginzburg models

Cited by in corpus (2)

• Some remarks on the group of derived autoequivalences
• The group of autoequivalences and the Fourier-Mukai number of a projective manifold