TITLE

ON THE LOCAL AND GLOBAL PRINCIPLE FOR SYSTEMS OF RATIONAL HOMOGENEOUS FORMS IN A FINITE NUMBER OF VARIABLES

AUTHOR(S)
Nguyen, Lan
PUB. DATE
February 2016
SOURCE
JP Journal of Algebra, Number Theory & Applications;Feb2016, Vol. 38 Issue 1, p79
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we prove that the Hasse principle for any system of rational cubic forms, any system of rational homogeneous forms of degree at least 3 in an arbitrary number of variables is equivalent to the Hasse principle of certain systems of rational quadratic forms. This shows, in particular, the Hasse principle for any system of rational cubic forms or rational homogeneous forms of degree at least 3 in an arbitrary number of variables holds if and only if the intersection of the nonempty sets of nontrivial rational solutions of each quadratic form of the associated system of quadratic forms is nonempty.
ACCESSION #
112695762

 

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