A classification of \bm{Q}-curves with complex multiplication

• NAKAMURA Tetsuo

  Mathematical Institute Tohoku University

Bibliographic Information

Other Title

• A classification of Q-curves with complex multiplication
• classification of Q curves with complex multiplication

Abstract

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 H²(H/\bm{Q}, ± 1). The structures of the abelian varieties over \bm{Q} obtained from \bm{Q}-curves by restriction of scalars are investigated.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 56 (2), 635-648, 2004

  The Mathematical Society of Japan

Keywords

• Q-curve
• elliptic curve
• complex multiplication
• embedding problem
• restriction of scalars

Details

• CRID: 1390282680091871360
• NII Article ID: 10013123220
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/1191418649
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2048478
• NDL BIB ID: 6928452
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I6928452
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed