2002/11/29 by Hans Schoutens
Mathematics · #math.AC #math.LO #math.RA #msc:13D22 #msc:13A35 #msc:03H05 #msc:13L05
published as C. R. Acad. Sci. Paris 336 (2003), 463-466 · Survey paper
arxiv created 2002/11/29 · arxiv updated 2009/11/30
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.