A classification of Q-curves with complex multiplication

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概要

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• Let H be the Hilbert class field of an imaginary quadratic field K. An elliptic curve E over H with complex multiplication by K is called a \bm{Q}-curve if E is isogenous over H to all its Galois conjugates. We classify \bm{Q}-curves over H, relating them with the cohomology group H<SUP>2</SUP>(H/\bm{Q}, ± 1). The structures of the abelian varieties over \bm{Q} obtained from \bm{Q}-curves by restriction of scalars are investigated.

• 一般社団法人 日本数学会の論文
• 2004-04-01

著者

• Nakamura Tetsuo

  Mathematical Institute Tohoku University

関連論文

• A classification of Q-curves with complex multiplication

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