ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 11E04, 11E81 Rehmann, Ulf, Universität Bielefeld, Germany Higher anisotropic kernels of quadratic forms Let q be an anisotropic regular quadratic form over a field k of any characteristic. The higher anisotropic kernels of q are natural algebraic invariants of q, occuring over the fields of a generic splitting tower of q. Theorem: The higher anisotropic kernel forms of q are definable over some purely transcendental extension of the ground field k, more precisely: There is a tower of purely transcendental field extensions k′_{0} = k ⊂ … ⊂ k′_{h} and a generic splitting tower k_{0} = k ⊂ … ⊂ k_{h} of q, such that k′_{i} ⊂ k_{i} is a multiquadratic extension, and such that the anisotropic kernel of q ⊗_{k} k_{i} is definable over k′_{i} for i = 0, …, h. This is some joint work with Manfred Knebusch.