The 3 Pfister number of quadratic forms

**Speaker**: M. Raczek (Université Catholique de Louvain)

**Time**: 3:00PM**Date**: Wed 27th October 2010

**Location**: Mathematical Sciences Seminar Room

**Abstract**

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.)

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