Non-commutative Iwasawa theory of elliptic curves at primes of multiplicative reduction
نویسندگان
چکیده
منابع مشابه
Iwasawa Theory of Elliptic Curves at Supersingular Primes over Zp-extensions of Number Fields
In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Zp-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi [9] and Perrin-Riou [17], we define restricted Selmer groups and λ±, μ±-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in terms ...
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Let E be an elliptic curve over Q and let p ≥ 5 be a prime of good supersingular reduction for E. Let K be an imaginary quadratic field satisfying a modified “Heegner hypothesis” in which p splits, write K∞ for the anticyclotomic Zp-extension of K and let Λ denote the Iwasawa algebra of K∞/K. By extending to the supersingular case the Λ-adic Kolyvagin method originally developed by Bertolini in...
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The topics that we will discuss have their origin in Mazur’s synthesis of the theory of elliptic curves and Iwasawa’s theory of ZZp-extensions in the early 1970s. We first recall some results from Iwasawa’s theory. Suppose that F is a finite extension of Q and that F∞ is a Galois extension of F such that Gal(F∞/F ) ∼= ZZp, the additive group of p-adic integers, where p is any prime. Equivalentl...
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We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Zp-extension of the CM field, where p is a prime of good, ordinary reduction for E. When the complex L-function of E vanishes to even order, Rubin’s proof the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the p-power Selmer group over the anticyclotomic extension is a torsion Iwasawa ...
متن کاملThe main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes
We develop the plus/minus p-Selmer group theory and plus/minus padic L-function theory for an elliptic curve E with complex multiplication over an abelian extension F of the imaginary quadratic field K given by the complex multiplication of E when p is a prime inert over K/Q (i.e. supersingular). As a result, we prove that the characteristic ideal of the Pontryagin dual of the plus/minus p-Selm...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2012
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004112000564