iwasawa module
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2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Cornelius Greither ◽  
Takenori Kataoka ◽  
Masato Kurihara

AbstractWe completely calculate the Fitting ideal of the classical p-ramified Iwasawa module for any abelian extension K/k of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former results where we had to assume that only p-adic places may ramify in K/k. One of the important ingredients is the computation of some complexes in appropriate derived categories.


2019 ◽  
Vol 100 (2) ◽  
pp. 245-255
Author(s):  
AMALA BHAVE ◽  
LACHIT BORA

Let $E$ be an elliptic curve over $\mathbb{Q}$ without complex multiplication. Let $p\geq 5$ be a prime in $\mathbb{Q}$ and suppose that $E$ has good ordinary reduction at $p$. We study the dual Selmer group of $E$ over the compositum of the $\text{GL}_{2}$ extension and the anticyclotomic $\mathbb{Z}_{p}$-extension of an imaginary quadratic extension as an Iwasawa module.


2017 ◽  
Vol 13 (03) ◽  
pp. 619-631 ◽  
Author(s):  
Takenori Kataoka

Let [Formula: see text] be a prime number. For a number field [Formula: see text], let [Formula: see text] be the compositum of all [Formula: see text]-extensions of [Formula: see text]. Then Greenberg’s generalized conjecture (GGC) claims that the unramified Iwasawa module [Formula: see text] is pseudo-null over the Iwasawa algebra associated to the Galois group of [Formula: see text]. In this paper, we establish sufficient conditions of GGC when [Formula: see text] is a complex cubic field and give many examples which satisfy the conditions with the help of computer programs.


2012 ◽  
Vol 154 (2) ◽  
pp. 303-324 ◽  
Author(s):  
CHERN–YANG LEE

AbstractThis paper studies the compact p∞-Selmer Iwasawa module X(E/F∞) of an elliptic curve E over a False Tate curve extension F∞, where E is defined over ℚ, having multiplicative reduction at the odd prime p. We investigate the p∞-Selmer rank of E over intermediate fields and give the best lower bound of its growth under certain parity assumption on X(E/F∞), assuming this Iwasawa module satisfies the H(G)-Conjecture proposed by Coates–Fukaya–Kato–Sujatha–Venjakob.


2010 ◽  
Vol 135 (1-2) ◽  
pp. 91-106 ◽  
Author(s):  
Ali Mouhib ◽  
Abbas Movahhedi
Keyword(s):  

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