Mixed characteristic homological theorems in low degrees

✍ Scribed by Hans Schoutens

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 89 KB
• Volume: 336
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(03)00114-6

✦ Synopsis

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.