Local Cohomology of Module of Differentials of integral extensions II.

In this note (R , m) denotes a complete regular local ring and B mostly denotes its absolute integral closure. The four objectives of this paper are the following: i) to determine the highest non-vanishing local cohomology of Ω B / R in equicharacteristic 0, ii) to establish a connection between each of Ω B / R and Ω B / V and pull-back of Ω A / V via a short exact sequence together with new observations on corresponding local cohomologies in mixed characteristic where V is the coefficient ring of R and A is its absolute integral closure, iii) to demonstrate that Ω B / R can be mapped onto a cohomologically Cohen-Macaulay module and iv) to study torsion-free property for Ω C / V and Ω C / k along with their respective completions where C is an integral domain and a module finite extension of R. In this connection an extension of Suzuki's theorem on normality of complete intersections to the formal set-up in all characteristics is accomplished. [ABSTRACT FROM AUTHOR]