Arithmetic models for Shimura varieties

TL;DR

This paper discusses recent advances in constructing well-behaved arithmetic models for a broad class of Shimura varieties and reports progress in understanding their properties.

Contribution

It introduces new methods for constructing arithmetic models of Shimura varieties and advances the study of their arithmetic properties.

Findings

Successful construction of arithmetic models for large classes of Shimura varieties

Progress in understanding the arithmetic properties of these models

Development of techniques applicable to broader classes of varieties

Abstract

We describe recent work on the construction of well-behaved arithmetic models for large classes of Shimura varieties and report on progress in the study of these models.