Arithmetic Geometry and Number Theory RTG Seminar: On Shimura varieties for unitary groups

Seminar | October 22 | 3-5 p.m. | 748 Evans Hall

 Brian Smithling, Johns Hopkins

 Department of Mathematics

Shimura varieties attached to unitary similitude groups are a well-studied class of PEL Shimura varieties (i.e., varieties admitting a moduli description in terms of abelian varieties endowed with a polarization, endomorphisms, and a level structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.