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Field theory and the Cohomology of Some Galois Groups

Alejandro Adem·Wenfeng Gao·Dikran Karagueuzian·Jan Minac
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Abstract

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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Alejandro Adem, Wenfeng Gao, Dikran Karagueuzian, Jan Minac. 2000-09-01. Field theory and the Cohomology of Some Galois Groups. https://arxiv.org/abs/math/0009011

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