Displaying similar documents to “Torsion points on abelian varieties of CM-type”

Abelian varieties over fields of finite characteristic

Yuri Zarhin (2014)

Open Mathematics

Similarity:

The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.

A Note on height pairings on polarized abelian varieties

Valerio Talamanca (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Let A be an abelian variety defined over a number field k . In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.

On the p-rank of an abelian variety and its endomorphism algebra.

Josep González (1998)

Publicacions Matemàtiques

Similarity:

Let A be an abelian variety defined over a finite field. In this paper, we discuss the relationship between the p-rank of A, r(A), and its endomorphism algebra, End(A). As is well known, End(A) determines r(A) when A is an elliptic curve. We show that, under some conditions, the value of r(A) and the structure of End(A) are related. For example, if the center of End(A) is an abelian extension of Q, then A is ordinary if and only if End(A) is a commutative field. Nevertheless, we give...

Isogeny orbits in a family of abelian varieties

Qian Lin, Ming-Xi Wang (2015)

Acta Arithmetica

Similarity:

We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.