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June 2017 Certain Forms Violate the Hasse Principle
Dong Quan Ngoc NGUYEN
Tokyo J. Math. 40(1): 277-299 (June 2017). DOI: 10.3836/tjm/1502179228

Abstract

A family of smooth geometrically irreducible curves violates the Hasse principle if they have local points everywhere, but they possesses no global points. In this paper, we show how to construct non-constant algebraic families of forms of degree $4k$ that violate the Hasse principle. Some examples of non-constant algebraic families of forms of degrees 12 and 24 that violate the Hasse principle are given to illustrate the method.

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Dong Quan Ngoc NGUYEN. "Certain Forms Violate the Hasse Principle." Tokyo J. Math. 40 (1) 277 - 299, June 2017. https://doi.org/10.3836/tjm/1502179228

Information

Published: June 2017
First available in Project Euclid: 8 August 2017

zbMATH: 06787100
MathSciNet: MR3689991
Digital Object Identifier: 10.3836/tjm/1502179228

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 1 • June 2017
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