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

研究成果: ジャーナルへの寄稿記事

3 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)83-96
ページ数14
ジャーナルBulletin of the Korean Mathematical Society
50
発行部数1
DOI
出版物ステータス出版済み - 11 11 2013

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Torsion Points
Elliptic Curves
Surjectivity
Galois Representations
Irreducibility
Galois group
Prime number
Number field
Torsion
Modulo
Subgroup

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Torsion points of elliptic curves with bad reduction at some primes II. / Yasuda, Masaya.

:: Bulletin of the Korean Mathematical Society, 巻 50, 番号 1, 11.11.2013, p. 83-96.

研究成果: ジャーナルへの寄稿記事

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