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2002•Compositio MathematicaOpen access

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

Alexander Schmidt

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Abstract

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).

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What this paper is about

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).

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Available abstract

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).

Key concepts: Mathematics, Galois module, Galois group, Cohomological dimension, Ramification, Galois extension, Pure mathematics, Galois cohomology

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