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On some rationality properties of Hopf maps

Published online by Cambridge University Press:  22 January 2016

Takashi Ono
Takashi Ono*
Affiliation:
The Johns Hopkins University
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As is well known, the Hopf fibration S3 → S2 is the restriction of the map h: R4 → R3 given by , a system of three quadratic forms [2]. Since spheres and the map are defined by polynomials with coefficients in Q, the original setting can be considered as a localization at infinity of the underlying algebraic sets and morphism defined over Q. This makes one think of the arithmetic of the Hopf maps.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 55 , November 1974 , pp. 145 - 150
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Artin, E., Geometric Algebra, Interscience Publishers, New York, 1957.Google Scholar
[2] Hopf, H., Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche, Math. Ann. 104 (1931), 637–665.Google Scholar
[3] Ono, T., Hasse Principle for Hopf Maps (to appear).Google Scholar
[4] Witt, E., Theorie der quadratischen Formen in beliebigen Körpern, J. reine angew. Math. 176 (1937), 31–44.CrossRefGoogle Scholar