Totally positive extensions and weakly isotropic forms
- 37 Downloads
The aim of this article is to analyse a new field invariant, relevant to (formally) real fields, defined as the supremum of the dimensions of all anisotropic, weakly isotropic quadratic forms over the field. This invariant is compared with the classical u-invariant and with the Hasse number. Furthermore, in order to be able to obtain examples of fields where these invariants take certain prescribed values, totally positive field extensions are studied.
Classification (MSC 2000)11E04 11E81 12D15
Unable to display preview. Download preview PDF.
- 5.Hoffmann, D.W.: Dimensions of Anisotropic Indefinite Quadratic Forms, I. Documenta Math., Quadratic Forms LSU 2001 183–200 (2001)Google Scholar
- 6.Lam, T.Y.: Introduction to quadratic forms over fields. Graduate Studies in Mathematics, 67. American Mathematical Society, Providence, RI, 2005.Google Scholar
- 7.Pfister, A.: Quadratic Forms with Applications to Algebraic Geometry and Topology. London Math. Soc. Lect. Notes 217. Cambridge University Press, 1995Google Scholar
- 8.Pierce, R.S.: Associative algebras. Graduate Texts in Mathematics 88, Springer- Verlag, New York, 1982Google Scholar
- 9.Prestel, A.: Remarks on the Pythagoras and Hasse number of real fields. J. Reine Angew. Math. 303/304, 284–294 (1978)Google Scholar
- 10.Prestel, A.: Lectures on Formally Real Fields. Lecture Notes in Math. 1093, Springer-Verlag, Berlin, 1984Google Scholar
- 11.Scharlau, W.: Quadratic and Hermitian forms. Grundlehren Math. Wiss. 270, Springer-Verlag, Berlin, 1985Google Scholar