Seminar on Arithmetic Algebraic Geometry: Compactifications of PELtype Shimura varieties and Kuga families with ordinary loci, II (1)
 Date

2012730 10:00 
2012730 12:00
 Place
 Faculty of Science Building #4 Room 501

Speaker/Organizer
 Kaiwen 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 pintegral models of various algebraic compactifications of PELtype 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 quasiprojectivity using auxiliary good reduction models. If time permits, I will discuss some other ingredients important for applications to the construction of overconvergent cusp forms.