Hasse principle for three classes of varieties over global function fields

Abstract

We give a geometric proof that Hasse principle holds for the following varieties defined over global function fields: smooth quadric hypersurfaces in odd characteristic, smooth cubic hypersurfaces of dimension at least $4$ in characteristic at least $7$, and smooth complete intersections of two quadrics of dimension at least $3$ in odd characteristics. In Appendix A we explain how to modify a previous argument of the author to prove weak approximation for cubic hypersurfaces defined over function fields of curves over algebraically closed fields of characteristic at least $7$. In Appendix B we prove some corollaries of Kollár's results on the fundamental group of separably rationally connected varieties.

48 pages. Comments are welcome

References in corpus (1)

• Weak approximation for cubic hypersurfaces

Cited by in corpus (2)

• Quadratic points on intersections of two quadrics
• Retour sur l'arithmétique des intersections de deux quadriques, avec un appendice par A. Kuznestov