ABSTRACT
Let φ1 and φ2 be quadratic forms over a field K of characteristic different from 2. In this paper, we complete the proof of the following result : if , then φ1 is isotropic over K(φ2) and φ2 is isotropic over K(φ1) if and only if K(φ1) and K(φ2) are isomorphic over K. To this end, we introduce a generalization of neighbors of Pfister forms to multiples of Pfister forms and study some of their function field and isotropy properties. We also apply this results to the seven- and nine-dimensional cases of the quadratic Zariski cancellation problem.
Acknowledgments
I would like to thank my advisor, Detlev Hoffmann, for having suggested this problem. I also wish to express my gratitude to Burt Totaro for his interest in my work and his encouragement. I am grateful to the referee for numerous suggestions on how to improve this paper.