Newton strata in the loop group of a reductive group

TL;DR

This paper extends the concept of purity in Newton stratification to individual break points within the loop group of a reductive group, providing new insights into deformation theory and Newton polygons.

Contribution

It introduces a generalized purity result for a single break point of the Newton point in the context of local G-shtukas and loop groups, advancing understanding of Newton stratification.

Findings

Proves a generalized purity for a single break point of the Newton point.

Shows elements bounded by a dominant coweight satisfy a generalized Grothendieck conjecture.

Establishes new links between loop group elements and deformation theory.

Abstract

We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that elements of the loop group bounded by a given dominant coweight satisfy a generalization of Grothendieck's conjecture on deformations of p-divisible groups with given Newton polygons.