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On Variants of CM-triviality

Abstract : We introduce a generalization of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalizes one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.
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Submitted on : Tuesday, October 16, 2012 - 12:34:22 PM
Last modification on : Monday, June 28, 2021 - 2:26:06 PM
Long-term archiving on: : Thursday, January 17, 2013 - 5:35:08 AM

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Thomas Blossier, Amador Martin-Pizarro, Frank Olaf Wagner. On Variants of CM-triviality. Fundamenta Mathematicae, Instytut Matematyczny, Polskiej Akademii Nauk,, 2012, 219 (3), pp.253-262. ⟨10.4064/fm219-3-4⟩. ⟨hal-00702683v2⟩

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