Complete modules and torsion modules

By W. Dwyer, J. Greenlees. 2002

166 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9da4ee166b836b013235d938d86bec44d8c116fb

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Citations in the corpus

Homological and Homotopical Aspects of Torsion Theories (2007, methodology): “A similar approach was considered independently by Dwyer and Greenlees in [43], although all the main ideas are due to Keller [69].”
Morita theory in abelian, derived and stable model categories (2003, methodology): “h from [Kel94a], based on the (diﬀerential graded) endomorphism ring of a tilting complex. A similar approach to and more applications of Morita theory in derived categories can be found in the paper [DG02] by Dwyer and Greenlees. 3.1. The derived category. In this section, R is any ring. All chain ”
Local duality in algebra and topology (2015, methodology): “which go back to Grothendieck [Har67], and their subsequent generalizations to the topological setting by Greenleesand May[GM92, GM95]. Instead ofworkingin the derivedcategorylikeDwyerandGreenlees do [DG02], we will use the stable category of chain complexes as deﬁned in [Lur14], which has none of t”
Generating the Fukaya categories of Hamiltonian 𝐺-manifolds (2015, background): “This can be seen as a form of Koszul duality; analogous nilpotence conditions play a decisive role in establishing the convergence of Eilenberg-Moore spectral sequence [20]; see also [21].”
Topological Hochschild homology and cohomology of A∞ ring spectra (2006, methodology): “Their main tool is the following piece of Morita theory, a kind of double centralizer theorem which is an easy consequence of the theory developed in [16].”
Finiteness in derived categories of local rings (2004, background): “Indeed, the criterion for M being built from k is a special case of the preceding example, and once again we refer the reader to [12] for details.”
Colocalizing subcategories and cosupport (2010, result): “The result below, which establishes an equivalence between the category of p-local and p-complete objects and the category of p-local and p-torsion objects, may be viewed as extension of such an equivalence discovered by Dwyer and Greenlees [9], Theorem 2.”
On differential graded categories (2006, background): “Moreover, if X and Y are smooth and projective over Spec k, we have a canonical isomorphism in Hqe pardg(X ×k Y ) ∼− → RHom(pardg(X), pardg(Y )) where pardg denotes the full dg subcategory of Ddg whose objects are the perfect complexes.”
Depth and amplitude for unbounded complexes (2002, background): “[12] J. P. C. Greenlees, J. P.”
Nilpotence and descent in equivariant stable homotopy theory (2015, background): “9) of the Dwyer–Greenlees [26] equivalence between complete and torsion objects, which is due to Hovey–Palmieri–Strickland [38, Th.”
Parametrizing recollement data for triangulated categories (2009, background): “Keller’s Morita theory for derived categories [23], a generalization of some results of [11,21] and offers an unbounded and abstract version of S.”
Weight structures and simple dg modules for positive dg algebras (2010, background): “The interplay between these two descriptions is at the heart of the interpretation of Koszul duality for dg algebras (and categories) given in [18], cf. also [12] [13].”