2000/09/01 by Alejandro Ádem, Alejandro Adem, Wenfeng Gao +7
Mathematics · #20J06 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20J06
paper · pdf · doi:10.48550/arxiv.math/0009011
arxiv created 2000/09/01 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.