# Integral models of Siegel modular varieties with Gamma_1(p)-type level-structure

## Richard Shadrach (Michigan State)

The Siegel modular varieties are moduli spaces for abelian schemes with certain additional structures. Integral models of these varieties can be defined by posing a moduli problem over the p-adic integers. In the case of Gamma_1(p)-type level structure, we consider moduli problems that use "Oort-Tate generators" for certain group schemes. In this case I will construct explicit local models, i.e. simpler schemes which can be used to study local properties of the integral models. I will then use the local model for the Siegel modular variety of genus 2 to construct a resolution of the integral model which is regular with special fiber a divisor of nonreduced normal crossings.

Tuesday, April 8th, at 4:00pm in HBH 227

Return to talks from Spring 2014