Completely Faithful Selmer Groups over Kummer Extensions

By Kazuya Kato, Y. Hachimori, O. Venjakob. 2003

82 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2db1b077306387b7b6d68aed8621d00f67ee3c19

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Computations in non‐commutative Iwasawa theory (2005, unknown): “There is an explicit formula for χna(E/k) in terms of χcyc(E/k) due to Hachimori and Venjakob ([26], thm 4.1 and the note following it).”
Fine Selmer groups of elliptic curves over p-adic Lie extensions (2005, methodology): “For our second example, we take the false Tate curve extension (see [9]) F∞ = F(μp∞, α1/pn : n = 1, 2, .”
On the Birch-Swinnerton-Dyer quotients modulo squares (2006, background): “elliptic curves (ordinary at p) in such extensions has been studied in the context of non-commutative Iwasawa theory, see e.g. [ 17 , 7, 8].”
A noncommutative Weierstrass preparation theorem and applications to Iwasawa theory (2002, methodology): “But what is very striking is that those modules which occur most naturally in arithmetic ( see below and [15]), namely the modules which are finitely generated over Λ(H), are either faithful or pseudo-null.”
Root numbers, Selmer groups, and non-commutative Iwasawa theory (2010, background): “If α = 5, it is known [26] that X(E/F∞) = 0, and sE/Ln = sE/Fn = 0 (n ≥ 1).”
Root Numbers of Non‐Abelian Twists of Elliptic Curves (2005, methodology): “And in x 5, we use the formula to examine the behaviour of the analytic rank of an elliptic curve over sub)elds of the so-called false Tate curve p-adic Lie extension (see [10]).”
Regulator constants and the parity conjecture (2007, background): “Root numbers and parities of Selmer ranks in the last 3 cases have recently been studied by Mazur–Rubin [20, 21], Hachimori–Venjakob [ 15 ] and one of us (V.) [8], Rohrlich [31] and Coates–Fukaya–Kato–Sujatha [3]; see also Greenberg’s preprint [12].”