On the Hasse principle for quartic hypersurfaces

O. Marmon; P. Vishe

doi:10.1215/00127094-2019-0025

Abstract

We establish the Hasse principle for smooth projective quartic hypersurfaces of dimension greater than or equal to $28$ defined over $\mathbb{Q}$ .

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O. Marmon. P. Vishe. "On the Hasse principle for quartic hypersurfaces." Duke Math. J. 168 (14) 2727 - 2799, 1 October 2019. https://doi.org/10.1215/00127094-2019-0025

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Received: 20 December 2017; Revised: 19 December 2018; Published: 1 October 2019

First available in Project Euclid: 18 September 2019

zbMATH: 07131298

MathSciNet: MR4012347

Digital Object Identifier: 10.1215/00127094-2019-0025

Subjects:

Primary: 11D72

Secondary: 11P55 , 14G05

Keywords: analytic number theory , circle method , Forms in many variables , Hasse principle , quartic hypersurfaces , rational points

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