An analytic viewpoint on the Hasse principle

Abstract

Working on Berkovich analytic curves, we propose a geometric approach to the study of the Hasse principle over function fields of curves defined over a complete discretely valued field. Using it, we show the Hasse principle to be verified for certain families of projective homogeneous spaces. As a consequence, we also obtain said principle in the already known cases of quadratic forms and homogeneous varieties over unitary groups.