Fields whose torsion free parts divisible with trivial Brauer group

On the Brauer Group – Notes for a Trivial Notions Seminar

This talk is about the Brauer group, an object of startling use and ubiquity – it exists equally well in the realms of pure algebra, pure geometry and at all points in between. So perhaps a good introduction to it is by way of another object which shares the same honor: the Picard group of X , which classifies structures which are equally deserving of the name “line bundle” and “rank 1 projecti...

Two Torsion in the Brauer Group of a Hyperelliptic Curve

We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C1. In general, we show that a large (but in general proper) subgroup of the 2torsion classes are given by the construction. Examples ...

Semiregular group divisible designs whose duals are semiregular

ABSTRAC"T A construction method for semiregular group divisible designs is given. This method can be applied to yield many classes of (in general, non-symmetric) semiregular group divisible designs whose duals are semiregular group divisible. In particular, the method can be used to construct many classes of transversal designs whose duals are serniregular group divisible designs, but not trans...

A Superposition Calculus for Divisible Torsion-Free Abelian Groups

On Fields with Finite Brauer Groups

Let K be a field of characteristic 6= 2, let Br(K)2 be the 2primary part of its Brauer group, and let GK(2) = Gal(K(2)/K) be the maximal pro-2 Galois group of K. We show that Br(k)2 is a finite elementary abelian 2-group (Z/2Z), r ∈ N, if and only if GK(2) is a free pro-2 product of a closed subgroup H which is generated by involutions and of a free pro-2 group. Thus, the fixed field of H in K(...