Séminaire d'algèbre et de géométrie du 22-11-2024

Exposé de Nico Lorenz

Le 22-11-2024 à 15:30, en P108 et en ligne.

Pfister numbers over valued fields

Résumé

Let F be a field of characteristic not 2. The n-th power of the fundamental ideal Iⁿ(F) in the Witt ring of F is the ideal generated by the Witt classes of the n-fold Pfister form. For a given form q whose Witt class lies in I^ⁿ(F), we investigate the minimal number k such that there are n-fold Pfister forms p₁, .., p_k whose orthogonal sum is Witt equivalent to q, called the n-Pfister number of q. In this talk, we survey known results for n <= 3. Further we present recent results on the connection between Pfister numbers of a valued field and its residue field, in particular with respect to forms of low dimension and the asymptotic behaviour for growing dimension.