Seminars on Arithmetic Geometry Arithmetic compactifications of PEL-type Shimura varieties(1)-(2)

2007-08-28 10:00 - 2007-08-28 16:00
Faculty of Science Building #8 Room307
Kai-Wen Lan(Harvard University)
In these lectures we explain how to construct the toroidal and minimalcompactifications for smooth integral models of PEL-type Shimura varieties(as defined in the works of Kottwitz and many other people), using generalizationsof the techniques developped by Mumford and Faltings-Chai.The essentially new ingredient is the emphasis on level structures, realized by atechnical calculation of Riemann forms, which enables us to predict the level structures from the degeneration data, and hence enables us to construct the boundary charts over which there does exists a valid level structure.