The square sieve and a Lang-Trotter question for generic abelian varieties

JOURNAL OF NUMBER THEORY

卷:191

Article

Bloom, Samuel¹ 

[1] Univ Maryland, College Pk, MD 20742 USA

关键词: Abelian variety;    Endomorphism algebra;    Lang-Trotter Conjectures;    Galois representations;   

DOI  :  10.1016/j.jnt.2018.04.002

来源: Elsevier

【 摘 要 】

Let A be a g-dimensional abelian variety over Q whose adelic Galois representation has open image in GSp(2g) Z. We investigate the Frobenius fields Q(pi(p)) = End (A(p)) circle times Q of the reduction of A modulo primes p at which this reduction is ordinary and simple. We obtain conditional and unconditional asymptotic upper bounds on the number of primes at which Q(pi(p)) is a specified number field and, when A is two-dimensional, at which Q(pi(p)) contains a specified real quadratic number field. These investigations continue the investigations of variants of the Lang-Trotter Conjectures on elliptic curves. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free