Back to Departmental Colloquium: Spring 2011
Departmental Colloquium
Date: Tuesday, Mar 1, 2011
Time: 4:15PM
Location: JWB 335
Brian Smithling
University of Toronto
Title |
On local models for Shimura varieties |
Abstract |
Shimura varieties are arithmetically interesting algebraic varieties defined over number fields. A basic problem for them is to define and study “good” models of them over (localizations of) rings of integers, so that (for example) the equations defining them can be reduced mod p. Amongst the most accessible Shimura varieties are those that admit interpretations as moduli spaces of abelian varieties with additional structure; for certain of these, Rapoport and Zink have defined natural integral models and, moreover, reduced the local study of them to their local models, which are projective schemes defined purely in terms of linear algebra. I will present an overview of some aspects of the theory of local models, focusing in particular on cases in which the Rapoport-Zink models are not “good” ones. |
Number Theory
Algebraic Geometry
Commutative Algebra