Duke Mathematical Journal

Hasse principle for three classes of varieties over global function fields

Zhiyu Tian

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Abstract

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.

Article information

Source
Duke Math. J., Volume 166, Number 17 (2017), 3349-3424.

Dates
Received: 29 September 2015
Revised: 20 August 2016
First available in Project Euclid: 19 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1505808016

Digital Object Identifier
doi:10.1215/00127094-2017-0034

Mathematical Reviews number (MathSciNet)
MR3724220

Zentralblatt MATH identifier
06825582

Subjects
Primary: 14M22: Rationally connected varieties
Secondary: 14D10: Arithmetic ground fields (finite, local, global) 14M10: Complete intersections [See also 13C40]

Keywords
Hasse principle global function field rationally connected variety

Citation

Tian, Zhiyu. Hasse principle for three classes of varieties over global function fields. Duke Math. J. 166 (2017), no. 17, 3349--3424. doi:10.1215/00127094-2017-0034. https://projecteuclid.org/euclid.dmj/1505808016


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