On the ubiquity of Gorenstein rings
On the ubiquity of Gorenstein rings
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DOI：
10.1007/bf01112819
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发表时间：
1963-02
影响因子：
0.8
通讯作者：
H. Bass
中科院分区：
文献类型：
--
作者：
H. Bass
APIARY [23]和GORENSTEIN Eg]及SAMUEL [2]证明了：如果（2）是平面曲线上的一点，则nQ = 2dQ，其中dQ= dlmw ~ 0/9 Q，nQ= dim C ′ Q/~ Q，θ是Q的局部环，CQ是其正规化环，~ Q是其导体。这一条件已受到各种代数几何学家的关注，最近ROQUETTE [19]和BEI~格尔[52]已将其置于一个相当一般的代数环境中。此外，ROSENLICHT [24]证明了~ o= 2do当且仅当f2 b是秩为1的自由9，其中f2 b是在Q上正则的微分模（在ROSENLICHT意义下）。C2 V是V上n次微分形式的层，则。0 V是秩为1的局部自由层。设W是余维数q在其所有点处的子簇。如果W是非奇异的，则定义Dw，并且GROTHENDIECK已经表明，
APIARY [23~, and subsequently GORENSTEIN Eg] and SAMUEL [2 (r proved9 3-~ t that if (2 is a point on a plane curve then no= 2d Q, where dQ= dlmw0/9 Q and nQ= dim C'Q/~ Q, 9 being the local ring of Q, CQ its normalization, and~ Q the conductor. This condition has received attention from a variety of algebraic geometers, and recently ROQUETTE [19J and BEI~ GER [52 have put it in a rather general algebraic setting. Furthermore, ROSENLICHT [24~(see also [211) proved that~ o= 2do if, and only if, f2b is a free 9 of rank one, where f2b is the module of differentials regular at Q (in the sense of ROSENLICHT).If V is a non singular variety of dimension n and. C2 V the sheaf of differential forms of degree n on V, then. 0 V is a locally free sheaf of rank one. Let W be a subvariety of codimension q at all of its points. If W is non singular Dw is defined, and GROTHENDIECK has shown that