# Connected components of closed affine Deligne-Lusztig varieties

## TL;DR

This paper determines the connected components of closed affine Deligne-Lusztig varieties for split reductive groups at any parahoric level, advancing understanding of their geometric structure.

## Contribution

It provides a complete classification of connected components for these varieties, a significant step forward in the study of affine Deligne-Lusztig varieties.

## Key findings

- Connected components explicitly determined for all parahoric levels.
- Results apply to split reductive algebraic groups.
- Advances understanding of geometric structures in algebraic groups.

## Abstract

For split reductive algebraic groups, we determine the connected components of closed affine Deligne-Lusztig varieties of arbitrary parahoric level.