# The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication

```@article{Coates2005TheGM,
title={The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication},
author={John Coates and Takako Fukaya and K. Katō and Ramdorai Sujatha and Otmar Venjakob},
journal={Publications math{\'e}matiques de l'IH{\'E}S},
year={2005},
volume={101},
pages={163-208}
}```
• Published 16 April 2004
• Mathematics
• Publications mathématiques de l'IHÉS
Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Zp. We prove the existence of a canonical Ore set S* of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S*, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its p…
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