Vertical unramified Brauer groups of Galois normic bundles

Abstract

We compute the vertical unramified Brauer group of the Galois normic bundles, which are given by ${\mathrm{N}}_{K/k}(\mathbf{z})=P(x)$. Our main result gives combinatorial formulas for the vertical unramified Brauer groups in terms of the Galois group structure of $K/k$ and the irreducible factors of $P(x)$.

8 pages, comments are welcome