TORSION OF ABELIAN VARIETIES OVER LARGE ALGEBRAIC EXTENSIONS OF ℚ

Moshe Jarden, Sebastian Petersen

Research output: Contribution to journalArticlepeer-review

Abstract

Let K be a finitely generated extension of ℚ, and let A be a nonzero abelian variety over K. Let K̄ be the algebraic closure of K, and let Gal(K) = Gal(K̄/K) be the absolute Galois group of K equipped with its Haar measure. For each σ ∈ Gal(K), let K̄ (σ) be the fixed field of σ in K̄. We prove that for almost all σ ∈ Gal(K), there exist infinitely many prime numbers l such that A has a nonzero K̄(σ)-rational point of order l. This completes the proof of a conjecture of Geyer-Jarden from 1978 in characteristic 0.

Original languageEnglish
Pages (from-to)46-86
Number of pages41
JournalNagoya Mathematical Journal
Volume234
DOIs
StatePublished - 1 Jun 2019

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