Number Theory Seminar

Vanishing theorems (of Kodaira, Nakano, Kawamata, Viehweg, Esnault, ...) have long played a key role in birational geometry.

Recently one has seen new applications in arithmetic geometry, esp. on the cohomology of Shimura varieties (e.g. work of B. Stroh's and of ours with K.-W. Lan).

We review various vanishing theorems, and then present two new ones.  We will try to put more focus on the context and (arithmetic) applications.