Abstract
We present a vanishing theorem for automorphic line bundles on good reduction fibers of PEL-type Shimura varieties (including all noncompact ones). As a consequence, we deduce that for a good prime p no smaller than the dimension of a PEL-type Shimura variety, any mod p cusp form of positive cohomological parallel weight is liftable to characteristic zero.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1870-1879 |
| Number of pages | 10 |
| Journal | International Mathematics Research Notices |
| Volume | 2011 |
| Issue number | 8 |
| DOIs | |
| State | Published - 2011 |
Bibliographical note
Funding Information:The first author [K.-W. L.] was supported by the Qui Shi Science and Technology Foundation and by the National Science Foundation [DMS-0635607]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of these organizations.