Products of trees and ${\mathrm{PGL}}_2$-torsors over the punctured affine line

Andrei S. Rapinchuk, Igor A. Rapinchuk, Avinash Roy

The goal of this article is to present a computation of the Galois cohomology of the group $G={\mathrm{PGL}}_2$ over rings of Laurent polynomials. This computation recovers the mai…