Class rank of differential modules
A differential flag of a differential module is a bounded below filtration such that the differential maps every level of the filtration into the level below. The projective class of a differential module is the smallest length of a differential filtration with projective factors. One can similarly define other classes based on other types of modules. The main result is the class inequality (Corollary 4.2), stating that over commutative noetherian rings with big Cohen-Macaulay modules, a lower bound for the projective class of a finitely generated differential module is the super height of the annihilator of the homology of any of its retract. (The super height is the supremum of heights of the ideal over all commutative noetherian base changes.) As an application, a lower bound is obtained for the rank of finitely generated differential modules with free differential flag over commutative noetherian rings as the double of the annihilator of the super height of the annihilator of the homology of any of its retract.
projective class of differential modules
finitely generated modules over a commutative noetherian ring
homological algebra of differential modules
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