Irrational Hilbert-Kunz multiplicities
Algebraic Geometry
2013-05-28 v1 Commutative Algebra
Abstract
We interpret Hilbert-Kunz theory of a graded ring of positive characteristic in terms of Frobenius asymptotic of cohomology of vector bundles on projective varieties. With this method we show that for almost all prime numbers there exist three-dimensional quartic hypersurface domains and modules of finite length with irrational Hilbert-Kunz multiplicity. From this we deduce that also the Hilbert-Kunz multiplicity of a local noetherian domain might be an irrational number.
Cite
@article{arxiv.1305.5873,
title = {Irrational Hilbert-Kunz multiplicities},
author = {Holger Brenner},
journal= {arXiv preprint arXiv:1305.5873},
year = {2013}
}
Comments
are welcome