Jurgen Hurrelbrink, Nikita A. Karpenko, and Ulf Rehmann: The Minimal Height of Quadratic Forms of Given Dimension

jurgen@math.lsu.edu, karpenko@euler.univ-artois.fr, rehmann@mathematik.uni-bielefeld.de

Submission: 2004, Oct 6

Given an arbitrary $n$, we consider anisotropic quadratic forms of dimension $n$ over all fields of characteristic $\ne2$ and prove that the height of an excellent form (depending on $n$ only) is the (precise) lower bound of the heights of all forms.

2000 Mathematics Subject Classification: 11E04

Keywords and Phrases: quadratic forms over arbitrary fields, splitting patterns, generic splitting

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