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Generic expansion of an abelian variety by a subgroup
Author(s) -
d'Elbée Christian
Publication year - 2021
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202000017
Subject(s) - mathematics , endomorphism , abelian group , abelian variety , torsion subgroup , algebraically closed field , rank of an abelian group , pure mathematics , arithmetic of abelian varieties , torsion (gastropod) , abelian variety of cm type , elementary abelian group , variety (cybernetics) , algebraic number , algebra over a field , discrete mathematics , mathematical analysis , statistics , medicine , surgery
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 NSOP 1 and not simple. Note that there exist abelian varieties A with End ( A ) = Z of any genus.