On Effective Witt Decomposition and Cartan-Dieudonné Theorem
Document Type
Lecture
Department
Mathematics (CMC)
Publication Date
9-23-2004
Abstract
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.
Rights Information
© 2004 Lenny Fukshansky
Terms of Use & License Information
Recommended Citation
Fukshansky, Lenny. "On Effective Witt Decomposition and Cartan-Dieudonné Theorem." Number Theory Seminar, Texas A&M University, College Station, Texas. 23 September 2004.
Comments
This lecture was given during the Number Theory Seminar at Texas A&M University in September 2004, and during the West Coast Number Theory Conference in Las Vegas, NV, December 2004.
This lecture is related to an article by the author: "On Effective Witt Decomposition and Cartan-Dieudonné Theorem," from the Canadian Journal of Mathematics Volume 59, Number 6, pages 1284-1300.