Generic expansion of an abelian variety by a subgroup. Issue 4 (5th November 2021) - d'Elbée, Christian
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 End ( A ) = Z . The resulting theory is NSOP1 and not simple. Note that there exist abelian varieties A with End ( A ) = Z of any genus.