… e following theorem, which is one of the main results of this section, provides a
comparison between the flat dimensions of a relative Cohen–Macaulay module and its non-zero …

… Along the way, we establish (in 2.1) a result, about a flat local homomorphism of local rings
… a flat local homomorphism of local rings such that B/mB is Cohen–Macaulay of dimension d. …

… in the category D(Flat A), which we call F-total acyclicity. We define finiteness of an F-Gorenstein
flat dimension for any complex. We show that the F-Gorenstein flat dimension of a …

… For an R-module M, the ith local cohomology module of M … R such that dim R/I = 1, then the
local cohomology modules Hi … cohomology modules, see Lyubeznik’s interesting paper [23]. …

… In Section , we study the flat dimensions of local cohomology modules. In Corollary ., we …
projective dimension of M in terms of the flat dimensions of its local cohomology modules and, …

… -dimensional formal module over F p equipped with a level-m-structure. By work of Boyer (in
equal characteristic) and Harris and Taylor, the ℓ-adic étale cohomology of … Drinfeld modular …

… which most of the results about homological dimensions easily can be derived. In … cohomology
modules are not finitely generated. In Section 3 we define the depth and the dimension of …

… of 3-dimensional flat manifolds satisfying the hypotheses of Theorems A and B are found in
Auslander [lJ, Auslander and Markus [2J. In the case of a compact flat Riemannian manifold (…

… cohomology modules of A regarded as a module over itself, and prescribes the depth and
dimension of … The natural local homomorphism A -» B makes B a flat ,4-module. Let nte denote …

… Then r• consists of squarefree modules S( -F), so we have a flat complex Z(Homs(r•,ws))(1), …
But Ext1(S/It:;.,ws) is a CohenMacaulay module of dimension 3, and the module structure of …