Motives of Certain Hyperplane Sections of Milnor Hypersurfaces
Abstract
We construct a hyperplane section Y of a Milnor hypersurface associated to a regular semisimple endomorphism . Exploiting its structure as a hyperplane section of a projective bundle and its natural torus action, we give a motivic decomposition of Y, which encodes both the cellular structure of Y and the arithmetic of the eigenvalues of . This decomposition is proven without using the "nilpotence principle", that is to say there are no "phantoms".
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