On the growth of $\mu $-invariant in Iwasawa theory of supersingular elliptic curves
نویسندگان
چکیده
We provide a relation between the $\mu $-invariants of dual plus and minus Selmer groups for supersingular elliptic curves when we ascend from cyclotomic ${\mathbb Z}_p$-extension to Z}_p^2$-extension over an imaginary quadratic field.
منابع مشابه
Iwasawa 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
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 کاملPlus/minus Heegner Points and Iwasawa Theory of Elliptic Curves at Supersingular Primes
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...
متن کاملIwasawa 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 ...
متن کاملLectures on the Iwasawa Theory of Elliptic Curves
These are a very preliminary (and incomplete!) version of the author’s lectures for the 2018 Arizona Winter School on Iwasawa Theory.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2022
ISSN: ['0065-1036', '1730-6264']
DOI: https://doi.org/10.4064/aa200724-11-7