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Hilbert-Kunz theory for binoidsBatsukh, Bayarjargal 19 December 2014 (has links)
We develop Hilbert-Kunz theory in a combinatorial setting namely for binoids. We show that the Hilbert-Kunz multiplicity for commutative, finitely generated, semipositive, cancellative and reduced binoids exists and is a rational number. This implies that the corresponding Hilbert-Kunz multiplicity for the binoid algebras does not depend on the characteristic.
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Hilbert-Kunz functions of surface rings of type ADE / Hilbert-Kunz Funktionen zweidimensionaler Ringe vom Typ ADEBrinkmann, Daniel 27 August 2013 (has links)
We compute the Hilbert-Kunz functions of two-dimensional rings of type ADE by using representations of their indecomposable, maximal
Cohen-Macaulay modules in terms of matrix factorizations, and as first syzygy modules of homogeneous ideals.
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