Year: 2026
Type: preprint
Abstract: Over any number field with sufficiently many roots of unity, we construct homogeneous spaces of $\mathbf{SL}_n$ with finite geometric stabilizers of nilpotency class $2$, whose unramified algebraic Brauer group consists only of constant classes, and which has no rational point but has local points in every completion of the ground field. This provides the first known examples of failures of the Hasse principle for homogeneous spaces of connected linear algebraic groups that are detected only by transcendental Brauer classes. The construction builds on the failure of a global--local principle for cup-product decomposition, based on a previous idea of Borovoi and Kunyavskii.
Source: arXiv (Cornell University)
Author: Linh, Nguyen Manh
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164002732