Cyclic components of quotients of abelian varieties mod p

Cristian Virdol

Research output: Contribution to journalArticle

Abstract

Let A an abelian variety of dimension r, defined over Q. For p a rational prime, we denote by Fp the finite field of cardinality p. If A has good reduction at p, let A¯p be the reduction of A at p. Let Γ be a free subgroup of the Mordell–Weil group A(Q), and let Γp be the reduction of Γ at p. In this paper for abelian varieties of type I, II, III, and IV, under Generalized Riemann Hypothesis, Artin's Holomorphy Conjecture, and Pair Correlation Conjecture, we obtain asymptotic formulas for the number of primes p, with p≤x, for which the quotient [Formula presented] has at most 2r−1 cyclic components.

Original languageEnglish
JournalJournal of Number Theory
DOIs
Publication statusAccepted/In press - 2018 Jan 1

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Abelian Variety
Quotient
Riemann hypothesis
Asymptotic Formula
Galois field
Cardinality
Subgroup
Denote

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Cyclic components of quotients of abelian varieties mod p. / Virdol, Cristian.

In: Journal of Number Theory, 01.01.2018.

Research output: Contribution to journalArticle

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