Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

EQUIVALENCES OF BIRCH AND SWINNERTON-DYER CONJECTURES OVER NON-ABELIAN EXTENSIONS OF ORDER 27

  • Yu, Ho-Seog (Department of Applied Mathematics, Sejong University)
  • Received : 2007.09.30
  • Accepted : 2008.01.04
  • Published : 2008.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

By finding two characters of subgroups of the Heisenberg group $H_{27}$ whose induced characters are same, we prove that the Birch and Swinnerton-Dyer conjectures for two elliptic curves corresponding to the characters are equivalent.

Keywords

References

  1. J. S. Milne, On the arithmetic of abelian varieties, Invent. Math. 11 (1972), 177-190.
  2. J. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106. Springer-Verlag 1986.
  3. J. Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog, In: Seminaire Bourbaki, 1965-66, expose 306.
  4. H. Yu, Representations and factors of restriction of scalars, J. of Number Theory 109 (2004), 266-277. https://doi.org/10.1016/j.jnt.2004.06.017