Journal of Symbolic Logic

Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup

Alessandro Berarducci

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Abstract

By recent work on some conjectures of Pillay, each definably compact group in a saturated o-minimal structure is an extension of a compact Lie group by a torsion free normal divisible subgroup, called its infinitesimal subgroup. We show that the infinitesimal subgroup is cohomologically acyclic. This implies that the functorial correspondence between definably compact groups and Lie groups preserves the cohomology.

Article information

Source
J. Symbolic Logic, Volume 74, Issue 3 (2009), 891-900.

Dates
First available in Project Euclid: 16 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1245158089

Digital Object Identifier
doi:10.2178/jsl/1245158089

Mathematical Reviews number (MathSciNet)
MR2548466

Zentralblatt MATH identifier
1181.03042

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality 22E15: General properties and structure of real Lie groups 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]

Keywords
Cohomology groups o-minimality

Citation

Berarducci, Alessandro. Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup. J. Symbolic Logic 74 (2009), no. 3, 891--900. doi:10.2178/jsl/1245158089. https://projecteuclid.org/euclid.jsl/1245158089


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