TY - JOUR

T1 - Cohomology of formal group moduli and deeply ramified extensions

AU - Bondarko, M. V.

PY - 2003/7/1

Y1 - 2003/7/1

N2 - 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 MR 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 H1(K, F(Km)) = 0 imply that K is deeply ramified? The answer is positive.

AB - 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 MR 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 H1(K, F(Km)) = 0 imply that K is deeply ramified? The answer is positive.

UR - http://www.scopus.com/inward/record.url?scp=0038675200&partnerID=8YFLogxK

U2 - 10.1017/S0305004102006485

DO - 10.1017/S0305004102006485

M3 - Article

AN - SCOPUS:0038675200

VL - 135

SP - 19

EP - 24

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -