Local Cohomology of Module of Differentials of integral extensions

The main focus of this paper is on determining the highest non-vanishing local cohomology modules of \Omega_(B/R), \Omega_(B/V)(\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®. 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.