Diagonalizing the Frobenius
Commutative Algebra
2007-09-30 v2
Abstract
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.
Cite
@article{arxiv.0705.1251,
title = {Diagonalizing the Frobenius},
author = {Esben Bistrup Halvorsen},
journal= {arXiv preprint arXiv:0705.1251},
year = {2007}
}