  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.
