| Résume | In this talk we adapt the Witt theory of hermitian forms over a central simple algebras over fields of characteristic not 2, to hermitian pairs over fields of characteristic 2. Hermitian pairs are hermitian forms with an extra datum that is necessary to describe all simply connected simple groups of type $D_n$ in characteristic 2. In order to define useful and well-behaved cohomological invariants for hermitian pairs, we define them using unramified cohomology attached to the function field of the Severi-Brauer variety associated to the central simple algebra which is the base of our hermitian pairs. We obtain classifying invariants and related them to classical invariants in small degrees.
(This is a joint work with Yong Hu.) |
