Chuangtian Guan (William & Mary)

Abstract: The notion of level structures originates from the study of the moduli spaces of elliptic curves, which are known as modular curves. In particular, Katz and Mazur constructed integral models of modular curves by carefully defining the moduli problems of elliptic curves with level structures. In 2017, Kottwitz and Wake generalized the $\Gamma_1(p^n)$-level structure to general p-divisible groups using primitive elements. In this talk, we will show some explicit calculations of the $\Gamma_1(p)$-level structure on the Siegel threefold, and use these calculations to prove some properties of the universal $\Gamma_1(p)$-cover.