Torsion points of elliptic curves with bad reduction at some primes II

Masaya Yasuda

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3 Citations (Scopus)

Abstract

Let K be a number field and fix a prime number p. For any set S of primes of K, we here say that an elliptic curve E over K has S-reduction if E has bad reduction only at the primes of S. There exists the set BK,p of primes of K satisfying that any elliptic curve over K with BK,p-reduction has no p-torsion points under certain conditions. The first aim of this paper is to construct elliptic curves over K with BK,p reduction and a p-torsion point. The action of the absolute Galois group on the p-torsion subgroup of E gives its associated Galois representation PE,p modulo p. We also study the irreducibility and surjectivity of ρE,p for semistable elliptic curves with BK,p-reduction.

Original languageEnglish
Pages (from-to)83-96
Number of pages14
JournalBulletin of the Korean Mathematical Society
Volume50
Issue number1
DOIs
Publication statusPublished - Nov 11 2013
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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