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Cohomology of formal group moduli and deeply ramified extensions
Published online by Cambridge University Press: 26 June 2003
Abstract
The aim of this paper is to answer a question of Coates and Greenberg: let $F$ be a commutative $m$-dimensional formal group over the ring of integers of a local field $k$, and let $K$ be an algebraic extension of $k$ with infinite ramification index. Denote by ${\cal M}_{\Mbar}$ the maximal ideal in the ring of integers of the separable closure of $K$. Suppose that the height of $F$ is greater than $m$. Does $H^1 (K, F ({\cal M}{}^m_{\Mbar}))=0$ imply that $K$ is deeply ramified? The answer is positive.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 1 , July 2003 , pp. 19 - 24
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- 2003 Cambridge Philosophical Society
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