On the geometry of the Newton stratification

TL;DR

This paper provides an overview of recent advances in understanding the structure and geometry of Newton stratification in the reduction modulo p of Shimura varieties of Hodge type, focusing on non-emptiness, dimensions, and closure relations.

Contribution

It summarizes recent results and methods on the global structure of Newton stratification, highlighting group-theoretic approaches and geometric properties.

Findings

Non-emptiness of Newton strata

Dimensions of Newton strata determined

Closure relations among strata elucidated

Abstract

We give an expository overview over recent results on the global structure and geometry of the Newton stratification of the reduction modulo p of Shimura varieties of Hodge type with hyperspecial level structure. More precisely, we discuss non-emptiness, dimensions, and closure relations of Newton strata. We also explain the group-theoretic description and methods leading to their proofs.