Article

# On the Cohomology of Galois Groups Determined by Witt Rings

Department of Mathematics, University of Wisconsin, Madison, Wisconsin, 53706, f1E-mail: {adem,dikran}@math.wisc.eduf1; Department of Mathematics, University of Western Ontario, London, Ontario, Canada, N6A 5B7f2E-mail: minac@uwo.caf2

Advances in Mathematics (Impact Factor: 1.35). 08/1998; DOI: 10.1006/aima.1999.1847 - [Show abstract] [Hide abstract]

**ABSTRACT:**One of the fundamental questions in current field theory, related to Grothendieck's conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of fields containing all squares, using pro-2-Galois groups of nilpotency class at most 2, and of exponent at most 4. This work extends some powerful methods and techniques from formally real fields to general fields of characteristic not 2. - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper we provide calculations for the cohomology of certain p-groups, using topological methods. More precisely, we look at p-groups G defined as central extensions 1→V→G→W→1 of elementary abelian groups such that and the defining k-invariants span the entire image of the Bockstein. We show that if p>dimV−dimW+1, then the cohomology of G can be explicitly computed as an algebra of the form where is a polynomial ring on two-dimensional generators and A is the cohomology of a compact manifold which in turn can be computed as the homology of a Koszul complex. As an application we provide a complete determination of the cohomology of the universal central extension provided , where n=dimW.Journal of Pure and Applied Algebra 05/2001; · 0.58 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Dedicated to Professor John Labute with admiration, respect and friendship. Abstract. We introduce Auslander-Reiten sequences for group algebras and give several recent applications. The rst part of the paper is devoted to some funda- mental problems in Tate cohomology which are motivated by homotopy theory. In the second part of the paper we interpret Auslander-Reiten sequences in the context of Galois theory and connect them to some important arithmetic objects.Annales des Sciences Mathématiques du Québec. 01/2008; 32(2).

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