English

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

R2 v1 2026-06-24T10:31:39.690Z