M. Raczek (Université Catholique de Louvain)

will speak on

The 3 Pfister number of quadratic forms

Time: 3:00PM
Date: Wed 27th October 2010
Location: Mathematical Sciences Seminar Room [map]

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 $(d^2)/2$.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)

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