… results for the homological dimensions: flat dimension, injective dimension, CI-dimension,
and Gdimension; in the second we discuss a related asymptotic homological condition. We …

… homological dimensions of finitely generated Tor-rigid, test and testrigid, ie, both Tor-rigid and
test, modules … we prove that the projective dimension of a finitely generated R-module M is …

… \)-rigid modules over … rigid modules are the algebras of radical square zero (see [2]), but
this class is not large enough for our purposes. In this section we study the \(\tau \)-rigid modules …

Let S be a base scheme in characteristic p. Consider the crystalline Dieudonne module functor
D on the category of^-divisible groups over S to the category of Dieudonne crystals over S…

… homological properties of quantum homogeneous spaces, such as, the relations between the
injective, global and Hochschild cohomological dimensions … property and rigid Gorenstein …

… -Macaulay), can be used as test modules, which detect finite homological dimensions of …
modules. We show that every Ulrich module of dimension s over a local ring is (s+1)-Tor-rigid-…

… a topological refinement of modular forms, which we call {\em topological modular forms}.
At the Zurich ICM I sketched a program designed to relate topological modular forms to …

… dimension at most one in terms of τ-rigid modules. We show that every indecomposable
module over iterated tilted algebras of Dynkin type is τrigid. … on homological dimension which is …

… the homological dimension of A (we refer the reader to [1] for notation and basic homological
facts … of R-modules, and A an R-module, then C is rigid with respect to A if and only if Ĉ is …

… Auslander in [1] for the case of unramified regular local rings will, together with the finiteness
condition which we impose upon the homological dimensions of the modules involved, be …