The main focus of this paper is on determining the highest non-vanishing local cohomology modules of ${\mathrm{\Omega }}_{B/R},{\mathrm{\Omega }}_{B/V}({\mathrm{\Omega }}_{B/k})$ where R is either a complete regular local ring or a complete local normal domain with coefficient ring V (field k) and B is its integral closure in an algebraic extension of $Q(R)$. Similar problem is also studied over a normal domain R containing a field k of characteristic 0. In this connection new observations on the direct summand property for integral extensions are also presented.

中文翻译：

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积分扩展微分模块的局部同调

本文的主要重点是确定最高无消失的局部同调模块 ${\mathrm{\Omega }}_{乙/\mathrm{[R}}，{\mathrm{\Omega }}_{乙/\mathrm{伏特}}（{\mathrm{\Omega }}_{乙/ķ}）$其中R是一个完整的规则局部环或一个具有系数环V（字段k）的完整局部正态域，而B是其在的代数扩展中的积分闭包$问（\mathrm{[R}）$。在包含特征为0的场k的正态域R上，也研究了类似的问题。在这方面，还提出了关于积分扩展的直接求和性质的新观察。