A quaternionic construction of p-adic singular moduli

On the p-adic geometry of traces of singular moduli

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono ([5, Problem 7.30]). As our goal is just to illustrate how p-adic geometry can be used in this context, we focus on a relatively simple case, in the hope that others will try to obtain the strong...

ON p-ADIC PROPERTIES OF TWISTED TRACES OF SINGULAR MODULI

We prove that logarithmic derivatives of certain twisted Hilbert class polynomials are holomorphic modular forms modulo p of filtration p+1. We derive p-adic information about twisted Hecke traces and Hilbert class polynomials. In this framework we formulate a precise criterion for p-divisibility of class numbers of imaginary quadratic fields in terms of the existence of certain cusp forms modu...

Construction of p-adic Hurwitz spaces

Moduli spaces for Galois covers of p-adic Mumford curves by Mumford curves are constructed using Herrlich’s Teichmüller spaces, André’s orbifold fundamental groups, and Kato’s graphs of groups encoding ramification data of charts for Mumford orbifolds.

Explicit construction of the p-adic numbers

A Quaternionic Construction of E7

We give an explicit construction of the simply-connected compact real form of the Lie group of type E7, as a group of 28 × 28 matrices over quaternions, acting on a 28-dimensional left quaternion vector space. This leads to a description of the simply-connected split real form, acting on a 56dimensional real vector space, and thence to the finite quasi-simple groups of type E7. The sign problem...