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THE IMAGE OF THE GALOIS GROUP FOR SOME CRYSTALLINE REPRESENTATIONS
 

Summary: THE IMAGE OF THE GALOIS GROUP FOR
SOME CRYSTALLINE REPRESENTATIONS
Victor A.Abrashkin
Let K be the quotient field of the Witt vectors ring W (k), where k is an algebraically
closed field of characteristic p > 0 and # = Gal( •
K/K). If U is a #­invariant lattice
of a continuous Qp[#]­module V of finite Qp­dimension and the set S of characters of
the semisimple envelope of
U# Fp satisfies some additional properties, we introduce
the function nU : S×S -# Z#0 #{#}, which carries a considerable part of informa­
tion about the image HU of # in Aut Zp U . We describe functions nU coming from
crystalline modules V with Hodge­Tate weights from [0, p - 2] and find their explicit
expressions in terms of corresponding filtered modules. This result is applied to a
description of the image H T (G) , where T (G) is the Tate module of a 1­dimensional
formal group G of finite height defined over W (k).
Bibliography: 9 issues.
0. Introduction.
Let K be the quotient field of the Witt vectors ring W = W (k), where k is an
algebraically closed field of characteristic p > 0, and let # = Gal( •
K/K) be the

  

Source: Abrashkin, Victor - Department of Mathematical Sciences, University of Durham

 

Collections: Mathematics