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Field Theory and the Cohomology of Some Galois Groups

✍ Scribed by Alejandro Adem; Wenfeng Gao; Dikran B Karagueuzian; Ján Mináč

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
201 KB
Volume
235
Category
Article
ISSN
0021-8693

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✦ Synopsis

We prove that two arithmetically significant extensions of a field F coincide if w x and only if the Witt ring WF is a group ring ‫ޚ‬rn 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 1

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✍ Alejandro Adem; Dikran B Karagueuzian; Ján Mináč 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 494 KB

Let F denote a field of characteristic different from two. In this paper we describe the mod 2 cohomology of a Galois group G F (called the W-group of F) which is known to essentially characterize the Witt ring WF of anisotropic quadratic modules over F. We show that H\*(G F , F 2 ) contains the mod