Iwasawa theory for the anticyclotomic extension
نویسندگان
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 ...
متن کاملAnticyclotomic Iwasawa Theory of Cm Elliptic Curves Ii
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 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...
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...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1985
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1985.119.489