Wednesday, January 25
Milner 313, 12:30 PM
Title: Effective theorems for quadratic spaces over Q-bar
Abstract: Let N >=2 be an integer, F a quadratic form in N variables over Qbar, and Z contained in Qbar^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 Qbar 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 Qbar. If time allows, we will also discuss some related effective results on orthogonal decomposition and structure of isometries for a bilinear space over Qbar. This extends previous results of the author over number fields. All bounds on height are explicit.