Cyclic components of abelian varieties (mod)

Cristian Virdol

doi:10.1016/j.jnt.2015.08.015

Cyclic components of abelian varieties (mod)

Cristian Virdol

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Consider A an abelian variety of dimension r, defined over a number field F. For a finite prime of F, we denote by F the residue field at . If A has good reduction at , let A- be the reduction of A at . In this paper, under GRH, we obtain an asymptotic formula for the number of primes of F, with NF/Q≤x, for which A-(F) has at most 2. r- 1 cyclic components.

Original language	English
Pages (from-to)	426-433
Number of pages	8
Journal	Journal of Number Theory
Volume	159
DOIs	https://doi.org/10.1016/j.jnt.2015.08.015
Publication status	Published - 2016 Feb 1

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2015.08.015

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abstract = "Consider A an abelian variety of dimension r, defined over a number field F. For a finite prime of F, we denote by F the residue field at . If A has good reduction at , let A- be the reduction of A at . In this paper, under GRH, we obtain an asymptotic formula for the number of primes of F, with NF/Q≤x, for which A-(F) has at most 2. r- 1 cyclic components.",

author = "Cristian Virdol",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

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N2 - Consider A an abelian variety of dimension r, defined over a number field F. For a finite prime of F, we denote by F the residue field at . If A has good reduction at , let A- be the reduction of A at . In this paper, under GRH, we obtain an asymptotic formula for the number of primes of F, with NF/Q≤x, for which A-(F) has at most 2. r- 1 cyclic components.

AB - Consider A an abelian variety of dimension r, defined over a number field F. For a finite prime of F, we denote by F the residue field at . If A has good reduction at , let A- be the reduction of A at . In this paper, under GRH, we obtain an asymptotic formula for the number of primes of F, with NF/Q≤x, for which A-(F) has at most 2. r- 1 cyclic components.

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DO - 10.1016/j.jnt.2015.08.015

M3 - Article

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SP - 426

EP - 433

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Cyclic components of abelian varieties (mod)

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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