Local Cohomology of Module of Differentials of integral extensions

TL;DR

This paper investigates the highest non-vanishing local cohomology modules of modules of differentials in integral extensions, providing new insights into their structure and properties in algebraic geometry.

Contribution

It introduces new results on the local cohomology of modules of differentials in integral extensions and explores the direct summand property in this context.

Findings

Identification of highest non-vanishing local cohomology modules

New observations on the direct summand property for integral extensions

Results applicable to regular local rings and normal domains

Abstract

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(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.