Mixed characteristic homological theorems in low degrees

Details Mixed characteristic homological theorems in low degrees Mixed characteristic homological theorems in low degrees

2002-11-29

arxiv.org/abs/math/0211466v1

C. R. Acad. Sci. Paris 336 (2003), 463-466

Mathematics

Commutative Algebra

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Scientific paper

Let R be a locally finitely generated algebra over a discrete valuation ring V of mixed characteristic. For any of the homological properties, the Direct Summand Theorem, the Monomial Theorem, the Improved New Intersection Theorem, the Vanishing of Maps of Tors and the Hochster-Roberts Theorem, we show that it holds for R and possibly some other data defined over R, provided the residual characteristic of V is sufficiently large in terms of the complexity of the data, where the complexity is primarily given in terms of the degrees of the polynomials over V that define the data, but possibly also by some additional invariants.

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