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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

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