On the Homology of Completion and Torsion
By M. Porta, Liran Shaul, Amnon Yekutieli. 2010
125 citations recorded by the source corpus.
Let A be a commutative ring, and ${\mathfrak{a}}$ a weakly proregular ideal in A. This includes the noetherian case: if A is noetherian then any ideal in it is weakly proregular; but there are other interesting examples. In this paper we prove the MGM equivalence, which is an equivalence between the category of cohomologically ${\mathfrak{a}}$-adically complete complexes and the category of cohomologically ${\mathfrak{a}}$-torsion complexes. These are triangulated subcategories of the derived category of A-modules. Our work extends earlier work by Alonso–Jeremias–Lipman, Schenzel and Dwyer–Greenlees.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d2c94ef1267b23a2b7115df840127ef10e1740bd
How researchers see this paper
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In Algebra and Number Theory
- Amnon Yekutieli
- L. Positselski
- M. Porta
- Liran Shaul
- Michel van den Bergh
- Alexander I. Efimov
- D. Pomerleano
- Kevin Lin
In Geometry and Topology
- Amnon Yekutieli
- L. Positselski
- M. Porta
- Liran Shaul
- Michel van den Bergh
- D. Pomerleano
- Kevin Lin
- Andrei Căldăraru
In Mathematical Physics
- L. Positselski
- Amnon Yekutieli
- M. Porta
- Liran Shaul
- Michel van den Bergh
- D. Pomerleano
- Kevin Lin
- Andrei Căldăraru
Citations in the corpus
- Abelian right perpendicular subcategories in module categories (2017, background): “5], the latter condition holds when I ⊂ R is a weakly proregular ideal in the sense of [35, 20].”
- Cohomologically Cofinite Complexes (2012, methodology): “Before the proof, let us recall some notation from [11].”