Generic expansion of an abelian variety by a subgroup | Zendy

d'Elbée Christian | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research