New cases of p-adic uniformization

TL;DR

This paper establishes a new p-adic uniformization theorem for specific Shimura varieties linked to unitary similitude groups over totally real fields, utilizing an alternative modular interpretation of the Drinfeld p-adic halfplane.

Contribution

It presents a Cherednik style p-adic uniformization theorem for certain Shimura varieties, expanding the understanding of their p-adic properties and modular interpretations.

Findings

Proves a new p-adic uniformization theorem for specific Shimura varieties.

Utilizes an alternative modular interpretation of the Drinfeld p-adic halfplane.

Extends the theory of p-adic uniformization in the context of unitary similitude groups.

Abstract

We prove a Cherednik style $p$-adic uniformization theorem for Shimura varieties associated to certain groups of unitary similitudes of size two over totally real fields. Our basic tool is the alternative modular interpretation of the Drinfeld $p$-adic halfplane of our earlier paper (arXiv 1108.5713)