Diagonalizing the Frobenius

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Over a Noetherian, local ring R of prime characteristic p, the Frobenius functor F induces a diagonalizable map on certain quotients of rational Grothendieck groups. This leads to an explicit formula for the Dutta multiplicity, and it is shown that a weaker version of Serre's vanishing conjecture holds if only chi(F(X)) = p^{dim R}chi(X) for all bounded complexes X of finitely generated, projective modules with finite length homology.
Revised (simplified) version. 12 pages

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Commutative Algebra, 13A35, 13D22, 13H15, 14F17

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http://salesiana.dossiersoluciones.com/handle/123456789/138887

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.1251
 http://arxiv.org/abs/0705.1251

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arXiv