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ON THE TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER Q

김도형
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회보 (Bulletin of the KMS)|제49권 제1호|pp. 155-163

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참고문헌

키워드

elliptic curvesIwasawa theoryTate-Shafarevich groupgood ordinary reduction
주제분류수학

초록

Let E be an elliptic curve over Q. Using Iwasawa theory,we give what seems to be the rst general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the Zp-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.

Abstract

Let E be an elliptic curve over Q. Using Iwasawa theory,we give what seems to be the rst general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the Zp-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.

참고문헌 (7)

  1. G. Chinta, "Analytic ranks of elliptic curves over cyclotomic fields", J. Reine Angew. Math, 544, pp.13~24 (2002)
  2. J. Coates, "The Tate-Shafarevich group for elliptic curves with complex multiplication II", Milan J. Math, 78(2), pp.395~416 (2010)
  3. G. H. Hardy, "An Introduction to the Theory of Numbers, 5th edition" (1938), Oxford Science Publications
  4. K. Kato, "p-adic Hodge theory and values of zeta functions of modular forms", Asterisque, 295, pp.117~290 (2004)
  5. J. I. Manin, "Parabolic points and zeta functions of modular curves", Izv. Akad. Nauk SSSR Ser. Mat, 36, pp.19~66 (1972)
  6. B. Mazur, "On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer", Invent. Math, 84(1), pp.1~48 (1986)
  7. J. Silverman, "The Arithmetic of Elliptic Curves, 2nd edition", Graduate Texts in Mathe- matics, 106 (2008), Springer

관련 논문AI추천

ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER Q WHEN p IS SUPERSINGULAR김도형대한수학회 · 대한수학회보2013 · 제50권 제2호A conjecture of Gross and Zagier: case $E(\mathbb{Q})_{\rm{tor}} \cong \mathbb{Z}/2\mathbb{Z}$ or $\mathbb{Z}/4\mathbb{Z}$김태경, 변동호, 이동건대한수학회 · 대한수학회지2023 · 제60권 제5호RESIDUAL SUPERSINGULAR IWASAWA THEORY OVER QUADRATIC IMAGINARY FIELDSParham Hamidi대한수학회 · 대한수학회보2023 · 제60권 제4호Remarks on Greenberg's conjecture for Galois representations associated to elliptic curvesAnwesh Ray대한수학회 · 대한수학회지2025 · 제62권 제5호ON ELLIPTIC CURVES WHOSE 3-TORSION SUBGROUP SPLITS AS μ₃ ⊕ Z/3ZMasaya Yasuda대한수학회 · 대한수학회논문집2012 · 제27권 제3호Lifting of the unramified Iwasawa module오장헌강원경기수학회 · 한국수학논문집2019 · 제27권 제3호

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