An analytic viewpoint on the Hasse principle
Algebraic Geometry
2024-04-05 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.2203.16234,
title = {An analytic viewpoint on the Hasse principle},
author = {Vlerë Mehmeti},
journal= {arXiv preprint arXiv:2203.16234},
year = {2024}
}
Comments
28 pages, 4 figures; considerable simplification of Section 3; final version