Iwasawa theory for elliptic curves at supersingular primes

2003 ◽  
Vol 152 (1) ◽  
pp. 1-36 ◽  
Author(s):  
Shin-ichi Kobayashi
Keyword(s):  
Elliptic Curves ◽  
Iwasawa Theory ◽  
Supersingular Primes

scholarly journals Iwasawa theory for modular forms at supersingular primes

2011 ◽  
Vol 147 (3) ◽  
pp. 803-838 ◽  
Author(s):  
Antonio Lei
Keyword(s):  
Elliptic Curves ◽  
Modular Forms ◽  
Iwasawa Theory ◽  
Selmer Groups ◽  
Main Conjecture ◽  
Supersingular Primes

AbstractWe generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of the plus and minus Coleman maps for normalised new forms of arbitrary weights and relate Pollack’s p-adic L-functions to the plus and minus Selmer groups. In addition, by generalising works of Pollack and Rubin on CM elliptic curves, we prove the ‘main conjecture’ for CM modular forms.

EULER CHARACTERISTICS AS INVARIANTS OF IWASAWA MODULES

2002 ◽  
Vol 85 (3) ◽  
pp. 634-658 ◽  
Author(s):  
SUSAN HOWSON
Keyword(s):  
Elliptic Curves ◽  
Euler Characteristic ◽  
Lie Group ◽  
Iwasawa Theory ◽  
Subject Classification ◽  
Finitely Generated ◽  
Euler Characteristics ◽  
Primary 16E10 ◽  
Iwasawa Algebra

If $G$ is a pro-$p$, $p$-adic, Lie group containing no element of order $p$ and if $\Lambda (G)$ denotes the Iwasawa algebra of $G$ then we propose a number of invariants associated to finitely generated $\Lambda (G)$-modules, all given by various forms of Euler characteristic. The first turns out to be none other than the rank, and this gives a particularly convenient way of calculating the rank of Iwasawa modules. Others seem to play similar roles to the classical Iwasawa $\lambda $- and $\mu $-invariants. We explore some properties and give applications to the Iwasawa theory of elliptic curves.2000 Mathematical Subject Classification: primary 16E10; seconday 11R23.

scholarly journals On the μ-invariants in Iwasawa theory of elliptic curves

2004 ◽  
Vol 30 (1) ◽  
pp. 1-28
Author(s):  
Yoshitaka HACHIMORI
Keyword(s):  
Elliptic Curves ◽  
Iwasawa Theory
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