Computational techniques for sheaf cohomology of locally profinite sets

TL;DR

This paper computes sheaf cohomology for certain locally profinite sets using novel $k$-sheer partitions and reduces intermediate cohomology questions to top degree cases.

Contribution

It introduces $k$-sheer partitions and demonstrates a method to relate intermediate cohomology to top cohomology via cocycle limits.

Findings

Computed sheaf cohomology with $Z_2$ coefficients for a class of locally profinite sets.

Introduced $k$-sheer partitions to facilitate cohomology constructions.

Showed that intermediate cohomology questions can be reduced to top cohomology questions.

Abstract

We compute the sheaf cohomology with constant $\mathbb{Z}_2$ coefficients of a concrete class of locally profinite sets of independent interest. We introduce $k$-sheer partitions to aid in constructions. It is also shown that questions of intermediate cohomology degrees can be reduced to questions about top cohomology degrees by exhibiting nontrivial top cocycles as pointwise limits of coboundaries.