关于典范模的Betti序列的增长性
On the growth of the Betti sequence of the canonical module
摘要：
研究了Cohen-Macaulay局部环的标准模的Betti序列的增长性.这是一个悬而未决的问题是否这个序列增长指数时，环不是Gorenstein。我们肯定地回答了一类环的指数增长性的问题，并证明了增长一般不是极值的。作为增长性的一个应用，我们给出了具有典范模的Cohen-Macaulay环是Gorenstein环的判别准则。
英文摘要：
We study the growth of the Betti sequence of the canonical module of a Cohen-Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen-Macaulay ring possessing a canonical module to be Gorenstein.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
