Bounded contractions for affine buildings

TL;DR

This paper introduces a method to construct contractions in affine buildings with refined chamber structures, aiding in proving the exactness of certain resolutions across various depths.

Contribution

It presents a novel construction of contractions at each vertex in refined affine buildings, extending the applicability of Schneider-Stuhler resolutions.

Findings

Constructed contractions at each vertex in affine buildings.

Proved exactness of Schneider-Stuhler resolutions for arbitrary depth.

Enhanced understanding of affine building structures and their resolutions.

Abstract

We consider affine buildings with refined chamber structure. For each vertex in the refined chamber structure we construct a contraction, based at the vertex, that is used to prove exactness of Schneider-Stuhler resolutions of arbitrary depth.