Absolute integral closure in positive characteristic
Absolute integral closure in positive characteristic
复制标题
正特性绝对积分闭合
DOI：
10.1016/j.aim.2006.07.001
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发表时间：
2006
影响因子：
1.7
通讯作者：
G. Lyubeznik
中科院分区：
文献类型：
--
作者：
C. Huneke;G. Lyubeznik
设R是局部正特征Noether整环. Hochster和Huneke的一个定理[M.霍克斯特角Huneke，Infinite integral extensions and big Cohen-Macaulay algebras，Ann. of Math.135（1992）53-89]指出，如果R是优的，则R的绝对积分闭包是一个大Cohen-Macaulay代数。证明了若R是Gorenstein局部环的同态像，则该环的所有局部上同调（维数以下）在有限扩张中映射为零.结果，Hochster和Huneke的原始结果扩展到R是Gorenstein局部环的同态像的情况，并且在假设重叠的情况下，例如，完整的诺特局部域。
Let R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke [M. Hochster, C. Huneke, Infinite integral extensions and big Cohen–Macaulay algebras, Ann. of Math. 135 (1992) 53–89] states that if R is excellent, then the absolute integral closure of R is a big Cohen–Macaulay algebra. We prove that if R is the homomorphic image of a Gorenstein local ring, then all the local cohomology (below the dimension) of such a ring maps to zero in a finite extension of the ring. As a result there follow an extension of the original result of Hochster and Huneke to the case in which R is a homomorphic image of a Gorenstein local ring, and a considerably simpler proof of this result in the cases where the assumptions overlap, e.g., for complete Noetherian local domains.