Local Cohomology of Module of Differentials of integral extensions
Abstract
The main focus of this paper is on determining the highest non-vanishing local cohomology modules of (B/R), (B/V)((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.
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