JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON THE RATIO OF TATE-SHAFAREVICH GROUPS OVER CYCLIC EXTENSIONS OF ORDER p2
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 36, Issue 2,  2014, pp.417-424
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2014.36.2.417
 Title & Authors
ON THE RATIO OF TATE-SHAFAREVICH GROUPS OVER CYCLIC EXTENSIONS OF ORDER p2
Yu, Hoseog;
  PDF(new window)
 Abstract
Let A be an abelian variety defined over a number field K and p be a prime. Define . Let be the abelian variety defined over K associated to the polynomial and let Ш() denote the Tate-Shafarevich groups of over K. In this paper assuming Ш(A/F) is finite, we compute [Ш()][Ш()]/[Ш()] in terms of K-rational points of , and their dual varieties, where [X] is the order of a finite abelian group X.
 Keywords
Tate-Shafarevich group;abelian varieties;cyclic extension;
 Language
English
 Cited by
 References
1.
C. D. Gonzalez-Aviles, On Tate-Shafarevich groups of abelian varieties, Proc. Amer. Math. Soc. 128 (2000), 953-961. crossref(new window)

2.
J. S. Milne, On the arithmetic of abelian varieties, Inventiones Math. 17 (1972), 177-190. crossref(new window)

3.
J. S. Milne, Arithmetic Duality Theorems, Perspectives in Math. vol. 1. Academic Press Inc. 1986.

4.
Hwasin Park, Idempotent relations and the conjecture of Birch and Swinnerton-Dyer, In: Algebra and Topology 1990 (Taejon, 1990), 97-125.

5.
H. Yu, On Tate-Shafarevich groups over Galois extensions, Israel Journal of Math. 141 (2004), 211-220. crossref(new window)