ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ℚ WHEN p IS SUPERSINGULAR

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 50, Issue 2, 2013, pp.407-416
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2013.50.2.407

Title & Authors

ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ℚ WHEN p IS SUPERSINGULAR

Kim, Dohyeong;

Kim, Dohyeong;

Abstract

Let E be an elliptic curve over and be a prime of good supersingular reduction for E. Although the Iwasawa theory of E over the cyclotomic -extension of is well known to be fundamentally different from the case of good ordinary reduction at p, we are able to combine the method of our earlier paper with the theory of Kobayashi [5] and Pollack [8], to give an explicit upper bound for the number of copies of occurring in the -primary part of the Tate-Shafarevich group of E over .

Keywords

Iwasawa theory;supersingular prime;elliptic curves;Tate-Shafarevich group;

Language

English

References

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G. Chinta, Analytic ranks of elliptic curves over cyclotomic fields, J. Reine Angew. Math. 544 (2002), 13-24.

2.

J. Coates, Z. Liang, and R. Sujatha, The Tate-Shafarevich group for elliptic curves with complex multiplication II, Milan J. Math. 78 (2010), no. 2, 395-416.

3.

W. Duke, J. B. Friedlander, and H. Iwaniec, Bounds for automorphic L-functions. II, Invent. Math. 115 (1994), no. 2, 219-239.

4.

D. Kim, On the Tate-Shafarevich group of elliptic curves over $\mathbb{Q}$ , Bull. Korean Math. Soc. 49 (2012), no. 1, 155-163.

5.

S. Kobayashi, Iwasawa theory for elliptic curves at supersingular primes, Invent. Math. 152 (2003), no. 1, 1-36.