报告题目：Analogs of the Hasse Invariant
报告人：Dr. Raju Krishnamoorthy
报告时间：3月23日 9:00-11:00
报告地点：1518
摘要：
We'll use formal properties of "correspondences without a core" to give "conceptual" (i.e. non-computational) proofs of statements like the following.
1. Any two supersingular elliptic curves over /bar{F_p} are related by an l-primary isogeny for any l/neq p.
2. A Hecke correspondence of compactified modular curves is always ramified at at least one cusp.
3. There is no canonical lift of supersingular points on a (projective) Shimura curve. (In particular, this provides yet another conceptual reason why there is not a canonical lift of supersingular elliptic curves.)
To do this, we'll introduce the concepts of "invariant line bundles" and of "invariant sections" on a correspondence without a core. Then (1), (2), and (3) will be implied by the following:
Theorem 1: Let X<-Z->Y be a correspondence of curves without a core over a field k. There is at most one etale clump.
Theorem 2. Let X<-Z->Y be an etale correspondence of curves without a core over a field of characteristic 0. Then there are no clumps.
We'll end with several open questions