Bockstein cohomology of maximal Cohen–Macaulay modules over Gorenstein isolated singularities

Let [Formula: see text] be an excellent equi-charateristic Gorenstein isolated singularity of dimension [Formula: see text]. Assume the residue field of [Formula: see text] is perfect. Let [Formula: see text] be any [Formula: see text]-primary ideal. Let [Formula: see text] be the associated graded ring of [Formula: see text] with respect to [Formula: see text] and let [Formula: see text] be the extended Rees algebra of [Formula: see text] with respect to [Formula: see text]. Let [Formula: see text] be a finitely generated [Formula: see text]-module. Let [Formula: see text] be the associated graded ring of [Formula: see text] with respect to [Formula: see text] (considered as a [Formula: see text]-module). Let [Formula: see text] be the [Formula: see text]-Bockstein cohomology of [Formula: see text] with respect to [Formula: see text]-torsion functor. We show there exists [Formula: see text] depending only on [Formula: see text] such that if [Formula: see text] is any [Formula: see text]-primary ideal with [Formula: see text] and [Formula: see text] generalized Cohen–Macaulay then the Bockstein cohomology [Formula: see text] has finite length for [Formula: see text] for any maximal Cohen–Macaulay [Formula: see text]-module [Formula: see text].