Meets: W 13.15-15.00 in von Neumann 1.023.
During the semester we'll develop the theories of abelian varieties and derived categories as a geometric invariant in parallel; about halfway through, the two theories will converge, and we'll see that many of the classical results on abelian varieties are more naturally expressed and proved using the derived category. This will culminate in a classification due to Orlov and Polishchuk of those abelian varieties that have isomorphic derived categories, as well as a complete understanding of the group of derived autoequivalences.
The main references we'll be using are:
15.10.14: Overview (Ben). Notes.
22.10.14: Triangulated categories (Nicolas). Notes.
29.10.14: Complex tori (Emre). Notes.
05.11.14: Derived categories (Giovanni). Notes.
12.11.14: Abelian varieties (Angela). Notes.
19.11.14: Derived categories of varieties (Gabriel).
26.11.14: Line bundles on abelian varieties (Irfan). Notes.
03.12.14: Exact functors (Rostislav). Notes.
10.12.14: The dual abelian variety (Niels). Notes.
17.12.14: Mukai's theorem (Ana). Notes.
07.01.15: Orlov's criterion (Gregor). Notes.
14.01.15: The derived category of an elliptic curve (Irene).
21.01.15: Derived equivalences of abelian varieties I (Daniele). Notes.
28.01.15: Derived equivalences of abelian varieties II (Ignacio). Notes.
04.02.15: Autoequivalences of abelian varieties (Andre). Notes.
11.02.15: Further topics (Ben).