On Effective Witt Decomposition and Cartan-Dieudonné Theorem
A classical theorem of Witt states that a bilinear space can be decomposed into an orthogonal sum of hyperbolic planes, singular, and anisotropic components. I will discuss the existence of such a decomposition of bounded height for a symmetric bilinear space over a number field, where all bounds on height are explicit. I will also talk about an effective version of Cartan-Dieudonné theorem on representation of an isometry of a regular symmetrice bilinear space as a product of reflections. Finally, if time permits, I will show a special version of Siegel's Lemma for a bilinear space, which provides a small-height orthogonal decomposition into one-dimensional subspaces.
© 2004 Lenny Fukshansky
Fukshansky, Lenny. "On Effective Witt Decomposition and Cartan-Dieudonné Theorem." Number Theory Seminar, Texas A&M University, College Station, Texas. 23 September 2004.