Algebra and Geometry Seminar

Date:
-
Location:
POT 745
Speaker(s) / Presenter(s):
Luis Sordo Vieira

Title:  A brief introduction to quadratic spaces

Abstract:  The level s(k) of a field k is defined to be the minimum n such that x_1^2+x^2+\cdots+x_n^2+1=0 has a solution over k. It turns out that if s(k)<\infty, then s(k)=2^l for some l\in \mathbb{N}.  The proof is a beautiful application of Pfister forms.
 
On our way to prove this result, we will introduce basic concepts in algebraic quadratic form theory, including the pioneering work of Witt and Pfister.