Manfred Knebusch (Regensburg)

Abstract: A panoramic view on the specialization of quadratic forms over a field \(K\) under a place \(\lambda:K\to L \cup \infty\), with focus on the generic splitting behavior of the specialization \(\lambda_x(\varphi)\) of a form \(\varphi\) over \(K\) in the case that char \(L\)=2 (while maybe char \(K\)=0). The form \(\lambda_*(\varphi)\) may have a big quasilinear part, a case which almost never is discussed in the literature. While the leading form of \(\lambda_*(\varphi)\) is a Pfister form if \(QL(\lambda_*(\varphi))=0\), new forms come in if the quasilinear part is big. The classification of all forms of height 1 is widely open.