论文标题
开放基因座的结果
Open loci results for commutative DG-rings
论文作者
论文摘要
鉴于具有界定的dg型DG模块的有界的noetherian非阳性DG环，我们研究了其常规的Gorenstein和Cohen-Macaulay loci。我们提供了足够的条件，可以打开常规基因座，并表明戈伦斯坦基因座始终是打开的。但是，这两个基因座通常都是空的：我们表明，无论$ \ mathrm {h}^0（a）$有多好，有示例，$ a $的戈伦斯坦基因座是空的。然后，我们表明，具有界化DG模块的界面的Noetherian DG环的Cohen-Macaulay轨迹始终包含一个密集的开放集。我们的结果表明，在温和的假设下，最终在本地衍生的方案最终是Cohen-Macaulay的，但即使在非常好的情况下，它们也不必通常是Gorenstein。
Given a commutative noetherian non-positive DG-ring with bounded cohomology which has a dualizing DG-module, we study its regular, Gorenstein and Cohen-Macaulay loci. We give a sufficient condition for the regular locus to be open, and show that the Gorenstein locus is always open. However, both of these loci are often empty: we show that no matter how nice $\mathrm{H}^0(A)$ is, there are examples where the Gorenstein locus of $A$ is empty. We then show that the Cohen-Macaulay locus of a commutative noetherian DG-ring with bounded cohomology which has a dualizing DG-module always contains a dense open set. Our results imply that under mild hypothesis, eventually coconnective locally noetherian derived schemes are generically Cohen-Macaulay, but that even in very nice cases, they need not be generically Gorenstein.
