Diagonalizing the Frobenius

Details Diagonalizing the Frobenius Diagonalizing the Frobenius

2007-05-09

arxiv.org/abs/0705.1251v2

Mathematics

Commutative Algebra

Revised (simplified) version. 12 pages

Scientific paper

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.

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