SR 511

Let Q and P be projective quadrics over a field k. A basic geometric problem is to understand under which circumstances there exists a rational morphism from P to Q over k. On the other hand, it was already apparent from the foundational works of A. Pfister that the study of this problem has many important applications to the algebraic theory of quadratic forms (e.g. structure of the Witt ring, construction of fields which exhibit certain arithmetic properties). In the past two decades, a fruitful interaction of algebraic and geometric methods has led to significant progress in addressing this problem. In this talk, we will describe analogues of well-known results of D. Hoffmann, O. Izhboldin, N. Karpenko, A. Merkurjev and B. Totaro on rational morphisms between quadrics for the class of so-called quasilinear hypersurfaces (hypersurfaces defined by diagonal forms of degree p of fields of characteristic p > 0). The case of quasilinear quadrics was previously considered by D. Hoffmann, A. Laghribi and B. Totaro.

Stephen Scully

University of Nottingham