Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cone spanned by maximal Cohen-Macaulay modules and an application   The aim of this paper is to define the notion of the Cohen-Macaulay cone of a
Noetherian local domain R and to present its application to the theory of
Hilbert-Kunz functions. It has been shown in Kurano's paper "Numerical
equivalence defined on Chow groups of Noetherian local rings", Invent. Math.
(2004), that, with a mild condition on R, the numerical Grothendieck group is a
finitely generated torsion-free abelian group. The Cohen-Macaulay cone of R is
a cone in the numerical Grothendieck group spanned by cycles represented by
maximal Cohen-Macaulay modules. We study basic properties on the Cohen-Macaulay
cone in this paper. As an application, various examples of Hilbert-Kunz
functions in the polynomial type will be produced. Precisely, for any given
integers $\epsilon_i$= 0, -1 or 1 for d/2<i<d, where d = dim R, we shall
construct a d-dimensional Cohen-Macaulay local ring R (of characteristic p) and
a maximal primary ideal I of R such that the Hilbert-Kunz function of R is a
polynomial in p^n of degree d whose coefficient of $(p^n)^i$ is the product of
$\epsilon_i$ and a positive rational number for d/2< i<d. The existence of such
ring is proved by using Segre products to construct a Cohen-Macaulay ring such
that the Chow group of the ring is of certain simplicity and that test modules
exists for it.

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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin