Vertical unramified Brauer groups of Galois normic bundles

TL;DR

This paper computes the vertical unramified Brauer group of Galois normic bundles, providing combinatorial formulas based on Galois group structure and polynomial factors, advancing understanding in algebraic geometry and number theory.

Contribution

It introduces explicit combinatorial formulas for the vertical unramified Brauer groups of Galois normic bundles, linking algebraic structures to geometric invariants.

Findings

Derived formulas for the Brauer groups in terms of Galois groups and polynomial factors

Connected Galois group structure to geometric invariants of normic bundles

Enhanced computational tools for algebraic geometry applications

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 $P(x)$.