Generic expansion of an abelian variety by a subgroup

Mathematical Logic Quarterly 67 (4):402-408 (2021)
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Abstract

Let A be an abelian variety in an algebraically closed field of characteristic 0. We prove that the expansion of A by a generic divisible subgroup of A with the same torsion exists provided A has few algebraic endomorphisms, namely. The resulting theory is NSOP1 and not simple. Note that there exist abelian varieties A with of any genus.

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10.1002/malq.202000017

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Citations of this work

Independence over arbitrary sets in NSOP1 theories.Jan Dobrowolski, Byunghan Kim & Nicholas Ramsey - 2022 - Annals of Pure and Applied Logic 173 (2):103058.

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References found in this work

On model-theoretic tree properties.Artem Chernikov & Nicholas Ramsey - 2016 - Journal of Mathematical Logic 16 (2):1650009.
Generic expansion and Skolemization in NSOP 1 theories.Alex Kruckman & Nicholas Ramsey - 2018 - Annals of Pure and Applied Logic 169 (8):755-774.
Independence in generic incidence structures.Gabriel Conant & Alex Kruckman - 2019 - Journal of Symbolic Logic 84 (2):750-780.

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