Abstract
Abstract Using an analogue of Knebusch's generic splitting tower invariant in the theory of non-singular quadratic forms, we study the splitting behaviour of quasilinear (or Fermat-type) forms of degree p over fields of characteristic p > 0. Several new applications of our main results to the theory of quasilinear quadratic forms are provided, including an analogue of a theorem of Vishik relating to the existence of outer excellent connections in the motives of smooth projective quadrics over fields of characteristic different from 2, partial results towards a quasilinear version of Karpenko's theorem on the possible values of the first higher Witt indices of non-singular quadratic forms in characteristic not 2, and a proof of a conjecture of Hoffmann concerning quadratic forms with maximal splitting in the quasilinear case.
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Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
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