Elliptic curves with surjective adelic galois representations

Aaron Greicius*

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Let K be a number field. The Gal(K̄/K)-action on the torsion of an elliptic curve E/K gives rise to an adelic representation ρE :Gal(K̄/K) → GL2(ℤ̂). From an analysis of maximal closed subgroups of GL2(ℤ̂) we derive useful necessary and sufficient conditions for ρE to be surjective. Using these conditions, we compute an example of a number field K and an elliptic curve E/K that admits a surjective adelic Galois representation.

Original languageEnglish (US)
Pages (from-to)495-507
Number of pages13
JournalExperimental Mathematics
Volume19
Issue number4
DOIs
StatePublished - Dec 1 2010

Keywords

  • Adelic
  • Elliptic curves
  • Galois representations
  • Maximal subgroups
  • Profinite
  • Torsion
  • ℓ-adic

ASJC Scopus subject areas

  • Mathematics(all)

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