Journal of Symbolic Logic

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

Alessandro Berarducci

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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

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

First available in Project Euclid: 16 June 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Cohomology groups o-minimality


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.

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