Isotropy of virtual Albert forms over function fields of quadrics, by Oleg Izhboldin and Nikita Karpenko

Let phi be a virtual Albert form over a field of characteristic different from 2, i.e. an anisotropic 6-dimensional quadratic form which remains anisotropic over the extension of the base field given by the squareroot of the discriminant. We give a complete description of the quadratic forms psi such that phi becomes isotropic over the function field of psi. This completes a series of works of Hoffmann, Laghribi, Leep, and Merkurev where the question was considered previously.


Oleg Izhboldin <karpenk@math.uni-muenster.de>
Nikita Karpenko <oleg@mpim-bonn.mpg.de>