Anticyclotomic Iwasawa theory of CM elliptic curves
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چکیده
منابع مشابه
Anticyclotomic Iwasawa Theory of Cm Elliptic Curves
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 ...
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We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Zpextension D∞ of the CM field K, where p is a prime of good, supersingular reduction for E. Our main result yields an asymptotic formula for the corank of the p-primary Selmer group of E along the extension D∞/K.
متن کاملAnticyclotomic Iwasawa Theory of Cm Elliptic Curves Ii Adebisi Agboola and Benjamin Howard
We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Zpextension D∞ of the CM field K, where p is a prime of good, supersingular reduction for E. Our main result yields an asymptotic formula for the corank of the p-primary Selmer group of E along the extension D∞/K.
متن کاملAnticyclotomic Iwasawa Theory of Cm Elliptic Curves Adebisi Agboola and Benjamin Howard with an Appendix by Karl Rubin
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 of 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 Iwasa...
متن کاملIwasawa Theory for Elliptic Curves
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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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2006
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2206