Hasse principle for hermitian spaces over semi-global fields

JOURNAL OF ALGEBRA

卷:458

Article

Wu, Zhengyao¹ 

[1] Emory Univ, Dept Math & Comp Sci, 400 Dowman Dr,W401, Atlanta, GA 30322 USA

关键词: Hermitian;    Hasse principle;    Local-global principle;    Isotropic;    Patching;    Projective homogeneous;    Twisted flag variety;   

DOI  :  10.1016/j.jalgebra.2016.02.027

来源: Elsevier

【 摘 要 】

In a recent paper, Colliot-Thelene, Parimala and Suresh conjectured that a local global principle holds for projective homogeneous spaces under connected linear algebraic groups over function fields of p-adic curves. In this paper, we show that the conjecture is true for any linear algebraic group whose almost simple factors of its semisimple part are isogenous to unitary groups or special unitary groups of hermitian or skew-hermitian spaces over central simple algebras with involutions. The proof implements patching techniques of Harbater, Hartmann and Krashen. As an application, we obtain a Springer-type theorem for isotropy of hermitian spaces over odd degree extensions of function fields of p-adic curves. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free