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 Bondal and Orlov.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1955-1971 |
| Number of pages | 17 |
| Journal | Advances in Mathematics |
| Volume | 230 |
| Issue number | 4-6 |
| DOIs | |
| State | Published - Jul 2012 |
| Externally published | Yes |
Bibliographical note
Funding Information:I would like to thank my adviser, Tony Pantev, for guiding me toward these ideas, endless patience, and extremely stimulating discussions. Without his help, I would not have even known where to begin. I would also like to thank Dmitri Orlov for several enlightening conversations and ideas, David Witt Morris for pointing out several references in the theory of arithmetic groups, and David Fithian for a useful discussion on modular forms. This work was funded by NSF Research Training Group Grant, DMS 0636606 .
Keywords
- Coherent sheaves
- Derived category
- Fourier-Mukai transform