greenberg’s conjecture
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2018 ◽  
Vol 292 (3) ◽  
pp. 633-639
Author(s):  
Ali Mouhib


2017 ◽  
Vol 13 (04) ◽  
pp. 1061-1070 ◽  
Author(s):  
Thong Nguyen Quang Do

For a totally real number field which is abelian over Q, in which an odd prime [Formula: see text] is totally split, and which verifies certain rather mild conditions on the cohomology of the circular units, we show that a weak form of Greenberg’s conjecture for [Formula: see text] holds true. This fills a gap — pointed out by René Schoof — in a previous proof (see Sur la conjecture faible de Greenberg dans le cas abélien [Formula: see text]-décomposé, Int. J. Number Theory 2(1) (2006) 49–64), and also extends the original result (semi-simplicity is no longer required).



2009 ◽  
Vol 148 (1) ◽  
pp. 93-106
Author(s):  
FILIPPO ALBERTO EDOARDO NUCCIO

AbstractFor a real abelian number field F and for a prime p we study the relation between the p-parts of the class groups and of the quotients of global units modulo cyclotomic units along the cyclotomic p-extension of F. Assuming Greenberg's conjecture about the vanishing of the λ-invariant of the extension, a map between these groups has been constructed by several authors, and shown to be an isomorphism if p does not split in F. We focus in the split case, showing that there are, in general, non-trivial kernels and cokernels.



2008 ◽  
Vol 136 (08) ◽  
pp. 2741-2744
Author(s):  
Luca Caputo ◽  
Filippo Alberto Edoardo Nuccio


2007 ◽  
Vol 122 (1) ◽  
pp. 121-134 ◽  
Author(s):  
Andrea Bandini


2005 ◽  
Vol 57 (4) ◽  
pp. 812-843
Author(s):  
Mak Trifković

AbstractLet E/ℚ be an elliptic curve with good ordinary reduction at a prime p > 2. It has a welldefined Iwasawa μ-invariant μ(E)p which encodes part of the information about the growth of the Selmer group ) as Kn ranges over the subfields of the cyclotomic Zp-extension K∞/ℚ. Ralph Greenberg has conjectured that any such E is isogenous to a curve E′ with μ(E′)p = 0. In this paper we prove Greenberg's conjecture for infinitely many curves E with a rational p-torsion point, p = 3 or 5, no two of our examples having isomorphic p-torsion. The core of our strategy is a partial explicit evaluation of the global duality pairing for finite flat group schemes over rings of integers.



2004 ◽  
Vol 113 (1) ◽  
pp. 1-14
Author(s):  
David C. Marshall


2003 ◽  
Vol 108 (4) ◽  
pp. 357-368 ◽  
Author(s):  
Andrea Bandini


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