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On the Relation between 2 and ∞ in Galois Cohomology of Number Fields

Published online by Cambridge University Press:  04 December 2007

Alexander Schmidt
Alexander Schmidt
Affiliation:
Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany; e-mail: schmidt@mathi.uni-heidelberg.de
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Abstract

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We remove the assumption ‘p≠ 2 or k is totally imaginary’ from several well-known theorems on Galois groups with restricted ramification of number fields. For example, we show that the Galois group of the maximal extension of a number field k which is unramified outside 2 has finite cohomological 2-dimension (also if k has real places).

Keywords

Galois cohomologyrestricted ramificationreal placescohomological dimension
Type
Research Article
Information
Compositio Mathematica , Volume 133 , Issue 3 , September 2002 , pp. 267 - 288
Copyright
© 2002 Kluwer Academic Publishers