Local-Global Principle for Unitary Groups Over Function Fields of p-adic Curves
Number Theory
2020-04-23 v1 Algebraic Geometry
Rings and Algebras
Abstract
Let K be a p-adic field and F the function field of a curve over K. Let G be a connected linear algebraic group over F of classical type. Suppose the prime p is a good prime for G. Then we prove that projective homogeneous spaces under G over F satisfy a local global principle for rational points with respect to discrete valuations of F . If G is a semisimple simply connected group over F , then we also prove that principal homogeneous spaces under G over F satisfy a local global principle for rational points with respect to discrete valuations of F.
Cite
@article{arxiv.2004.10357,
title = {Local-Global Principle for Unitary Groups Over Function Fields of p-adic Curves},
author = {R. Parimala and V. Suresh},
journal= {arXiv preprint arXiv:2004.10357},
year = {2020}
}