Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal Cohen-Macaulay modules over local toric rings   In analogy with the classical, affine toric rings, we define a local toric
ring as the quotient of a regular local ring modulo an ideal generated by
binomials in a regular system of parameters with unit coefficients; if the
coefficients are just $\pm1$, we call the ring purely toric.
  We prove the following results on the existence of MCM's (=maximal
Cohen-Macaulay modules): (EQUI$\mathstrut_p$) we construct certain families of
local toric rings satisfying Hochster's small MCM conjecture in positive
characteristic; (EQUI$\mathstrut_0$) provided Hochster's small MCM conjecture
holds in positive characteristic with the additional condition that the
multiplicity of the small MCM is bounded in terms of the parameter degree of
the ring, then any local ring (not necessarily toric) in equal characteristic
zero admits a formally etale extension satisfying Hochster's small MCM
conjecture (this applies in particular to the families from
(EQUI$\mathstrut_p$)); and (MIX), in mixed characteristic, we show that all
purely toric local rings satisfy Hochster's big MCM conjecture, and so do those
belonging to the families from (EQUI$\mathstrut_p$).

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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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: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph