Field theory and the Cohomology of Some Galois Groups

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We prove that two arithmetically significant extensions of a field F coincide if and only if the Witt ring WF is a group ring Z/n[G]. Furthermore, working modulo squares with Galois groups which are 2-groups, we establish a theorem analogous to Hilbert's Theorem 90 and show that an identity linking the cohomological dimension of the Galois group of the quadratic closure of F, the length of a filtration on a certain module over a Galois group, and the dimension over Z/2 of the square class group of the field holds for a number of interesting families of fields. Finally we discuss the cohomology of a particular Galois group in a topological context.

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Algebraic Topology, Group Theory, 20J06

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http://salesiana.dossiersoluciones.com/handle/123456789/59840

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0009011
 http://arxiv.org/abs/math/0009011

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arXiv