Tian, Zhiyu Hasse principle for three classes of varieties over global function fields. (English) Zbl 1451.14075 Duke Math. J. 166, No. 17, 3349-3424 (2017). Summary: We give a geometric proof that the Hasse principle holds for the following varieties defined over global function fields: smooth quadric hypersurfaces, smooth cubic hypersurfaces of dimension at least 4 in characteristic at least 7, and smooth complete intersections of two quadrics, which are of dimension at least 3, in odd characteristics. Cited in 4 Documents MSC: 14G12 Hasse principle, weak and strong approximation, Brauer-Manin obstruction 14M22 Rationally connected varieties 14D10 Arithmetic ground fields (finite, local, global) and families or fibrations 14M10 Complete intersections 14G05 Rational points Keywords:Hasse principle; global function field; rationally connected variety PDFBibTeX XMLCite \textit{Z. Tian}, Duke Math. J. 166, No. 17, 3349--3424 (2017; Zbl 1451.14075) Full Text: DOI arXiv