The Brauer Group of Quotient Spaces by Linear Group Actions

Rational Connectedness and Galois Covers of the Projective Line

“…By (1), there exists a nonconstant k-morphism ρ : S → U such that the pull-back of the G-torsor V → U under ρ is isomorphic to the G-torsor T /S. Given any α ∈ GL n (A), the G-torsor (α.ρ) * (V → U ) is G-isomorphic to the G-torsor T .…”

“…Saltman's work [18] (extended by Bogomolov [1], see [21, §7.6 and §7.7]) produces finite p-groups G together with faithful (finite dimensional) linear representations W of G over the complex field C, such that the unramified Brauer group Br nr (F ) of F = C(W ) G is a nontrivial (p-primary) group. Here by C(W ) we denote the fraction field of the symmetric algebra on W .…”

“…The idea of using a versal model of a G-torsor, originally due to E. Noether, has come up a number of times in the literature, notably in work of E. Fischer, D. Saltman [17], F. A. Bogomolov [1]; see [20] and [21] for further references.…”

Fields of Invariants of Finite Linear Groups

“…G is not stably rational [Bog88]. On the other hand, it is known that the field of invariant of any linear action of a p-group of order ≤ p 4 on k(x 1 , .…”

Bogomolov multipliers for some p-groups of nilpotency class 2

“…Definition 1.1. We say that a group G has the AEC (Abelian Extension of a Cyclic group) property if G has a normal abelian subgroup H such that the quotient group G/H is cyclic Bogomolov [4,Lemma 4.9] proved that if G has the AEC property then B 0 (G) = 0. On the other hand, Noether's problem for p-groups with the AEC property is still not solved entirely.…”