Seminar on Arithmetic Algebraic Geometry: Compactifications of PEL-type Shimura varieties and Kuga families with ordinary loci, II (2)

2012-7-30 14:00 - 2012-7-30 16:00
Faculty of Science Building #4 Room 501
Kai-wen Lan
During the Workshop on the Arithmetic Geometry of Shimura Varieties, Representation Theory, and Related Topics, from July 18th to 22nd, 2012, I talked about the constructions of normal flat p-integral models of various algebraic compactifications of PEL-type Shimura varieties and Kuga families, allowing both ramification and levels at p, with good behaviors over the loci where certain (multiplicative) ordinary level structures are defined.

I will briefly review the main statements, and give more details about the constructions, focusing on two important ingredients: I will explain about a theory of degeneration for (multiplicative) ordinary level structures (generalizing earlier works of Mumford, Faltings, Chai, some others, and myself), and some technique for proving quasi-projectivity using auxiliary good reduction models. If time permits, I will discuss some other ingredients important for applications to the construction of overconvergent cusp forms.