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arXiv · 1505.06548

Hasse principle for three classes of varieties over global function fields

Zhiyu Tian
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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 Koll\'ar's results on the fundamental group of separably rationally connected varieties.

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Zhiyu Tian. 2015-05-25. Hasse principle for three classes of varieties over global function fields. https://doi.org/10.1215/00127094-2017-0034

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