… a duality between homology and local cohomology modules for these modules. Another
important result of this work is to extend Grothendieck's vanishing and non-vanishing theorems …

… local homology modules. At first, we obtain the following main results about vanishing of local
homology modules. … we obtain a vanishing result of generalized local homology modules. …

… Ulrich modules as test modules for projective and injective dimensions. In Section 4, we provide
some results on the vanishing of Exts and Tors over CM local … By Matlis Duality, it can be …

… Our proof relies on a duality statement and the result on regularity by Trung and Wang in [21]. …
Let \(\Omega ^nM\) be the nth-syzygy module of M. Again by local duality and the claim we …

… on the theory of derived local homology and cohomology, we regretfully notice that there is
… that the Greenlees-May Duality generalizes the Local Duality in simple and traceable steps. …

… Herzog's theory of generalized local cohomology and explore its main aspects, eg, (non-)vanishing
results as well as a general local duality theorem which extends, to a much broader …

… In this case by using local duality, one can convert this into a … In this form, this is a question
of the vanishing of the local … something for all local cohomology modules past some value…

… and the ordinary generalized local cohomology modules. … the vanishing and non-vanishing
of generalized d-local … Suzuki, On the generalized local cohomology and its duality, J. …

… local cohomology and local homology functors satisfying an abstract version of local duality.
… in A, we recover the classical local duality due to Grothendieck as well as generalizations …

… 3.3, we use Drinfeld’s miraculous duality to compute the Serre functor on the DG category
\(\mathfrak {D}({\text {Bun}}_G({\mathbb {P}}^1))\). In Sect. 4, we compute the Serre functor of …