Document Type



Mathematics (CMC)

Publication Date



Let N >= 2 be an integer, F a quadratic form in N variables over (Q) over bar, and Z subset of (Q) over bar (N) an L-dimensional subspace, 1 <= L <= N. We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space (Z, F). This provides an analogue over (Q) over bar of a well-known theorem of Vaaler proved over number fields. We use our result to prove an effective version of Witt decomposition for a bilinear space over (Q) over bar. We also include some related effective results on orthogonal decomposition and structure of isometries for a bilinear space over (Q) over bar. This extends previous results of the author over number fields. All bounds on height are explicit.


Previously linked to as:,296.

Source: Author's post-print manuscript in pdf

Rights Information

© 2008 World Scientific Publishing Company.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Included in

Mathematics Commons