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Géométries relatives

Thomas Blossier 1 Amador Martin-Pizarro 1 Frank Olaf Wagner 1 
1 AGL - Algèbre, géométrie, logique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a subgroup of a product of groups definable in the reducts. In the relatively CM-trivial case, which contains certain Hrushovski amalgamations (the fusion of two strongly minimal sets or the expansions of a field by a predicate), every definable group allows a homomorphism with virtually central kernel into a product of groups definable in the reducts.
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Submitted on : Tuesday, May 21, 2013 - 10:18:11 AM
Last modification on : Monday, June 28, 2021 - 2:26:06 PM
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Thomas Blossier, Amador Martin-Pizarro, Frank Olaf Wagner. Géométries relatives. Journal of the European Mathematical Society, European Mathematical Society, 2015, 17 (2), pp.229-258. ⟨10.4171/JEMS/502⟩. ⟨hal-00514393v4⟩



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