The 3 Pfister number of quadratic forms
Speaker: M. Raczek (Université Catholique de Louvain)
Date: Wed 27th October 2010
Location: Mathematical Sciences Seminar Room
Let F be a field of characteristic different from 2 containing a square root of −1. The 3-Pfister number of a quadratic form q in the third power of the fundamental ideal of F, is the least number of terms needed to write q as a sum of 3-fold Pfister forms. We use a combinatorial analogue of the Witt ring of F to prove that, if F is a 2-henselian valued field with at most two square classes in the residue field, then the 3-Pfister number of a d-dimensional quadratic form is less than or equal to (d2)/2.
(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)