Invariance of o-minimal cohomology with definably compact supports

TL;DR

This paper establishes criteria for the invariance of o-minimal cohomology with definably compact supports across elementary extensions and expansions, and proves an analogue of Wilder's finiteness theorem within o-minimal structures.

Contribution

It introduces general criteria ensuring cohomology invariance and extends Wilder's finiteness theorem to o-minimal contexts.

Findings

Cohomology invariance criteria in o-minimal structures

Proof of o-minimal analogue of Wilder's finiteness theorem

Applicability to definable spaces with sheaf coefficients

Abstract

In this paper we find general criteria to ensure that, in an arbitrary o-minimal structure, the o-minimal cohomology without supports and with definably compact supports of a definable space with coefficients in a sheaf is invariant in elementary extensions and in o-minimal expansions. We also prove the o-minimal analogue of Wilder's finiteness theorem in this context.