Submission date: 23 May 2007

Abstract:

We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the intersection of a definable decreas-ing family of definably compact sets, under the additional assumption that the o-minimal structure expands a field.

Mathematics Subject Classification: 03C64, 14P25, 55N30

Keywords and phrases: O-minimality, spectrum, sheaf, Cech, cohomology

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