Markus Rost (Bielefeld)

Abstract: Pfister forms are important to understand Galois cohomology mod 2. There are generalizations of Pfister forms to any prime p.  These are easily written down, but are not forms and are not very "round" either. They are in fact not very canonical rational functions. However, for a given symbol in the Galois cohomology ring mod p, there is only one such function up to correspondences of degree prime to p. Their multiplicativity is known for base fields with no field extensions of degree prime to p.  The construction of these functions was very much influenced by the case p=2.