Noncommutative (Crepant) Desingularizations and the Global Spectrum of Commutative Rings
Noncommutative (Crepant) Desingularizations and the Global Spectrum of Commutative Rings
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DOI：
10.1007/s10468-014-9510-y
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发表时间：
2014-01
影响因子：
0.6
通讯作者：
Hailong Dao;Eleonore Faber;C. Ingalls
中科院分区：
文献类型：
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作者：
Hailong Dao;Eleonore Faber;C. Ingalls
本文研究未必正规交换环上的有限整体维数自同态环。这些对象最近引起了人们的注意，作为非交换（crepant）决议，或NC（C）Rs，奇点。我们提出了一个概念的NCCR在任何交换环，似乎较弱，但推广了所有以前的概念。我们的结果产生强有力的必要和充分条件存在这样的对象在许多情况下的利益。我们也给出了新的例子NCR的曲线奇点，正则局部环和正常的交叉奇点。此外，我们引入并研究了环R的整体谱，即MCMR-模的自同态环的所有可能的有限整体维数的集合。最后，我们利用各种方法计算了许多自同态环的整体维数。
In this paper we study endomorphism rings of finite global dimension over not necessarily normal commutative rings. These objects have recently attracted attention as noncommutative (crepant) resolutions, or NC(C)Rs, of singularities. We propose a notion of a NCCR over any commutative ring that appears weaker but generalizes all previous notions. Our results yield strong necessary and sufficient conditions for the existence of such objects in many cases of interest. We also give new examples of NCRs of curve singularities, regular local rings and normal crossing singularities. Moreover, we introduce and study the global spectrum of a ringR, that is, the set of all possible finite global dimensions of endomorphism rings of MCMR-modules. Finally, we use a variety of methods to compute global dimension for many endomorphism rings.