All tilting modules are of finite type
By Silvana Bazzoni, J. Št’ovíček. 2007
53 citations recorded by the source corpus.
We prove that any infinitely generated tilting module is of finite type, namely that its associated tilting class is the Ext-orthogonal of a set of modules possessing a projective resolution consisting of finitely generated projective modules.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/10aefd8cc53e865ead7a15f8d4fc4d97d37e0156
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In Algebra and Number Theory
- J. Št’ovíček
- Lidia Angeleri Hugel
- David Pospíšil
- Jan Trlifaj
- Apostolos Beligiannis
- Xiao-Wu Chen
- Mark Hovey
- Chrysostomos Psaroudakis
In Geometry and Topology
- J. Št’ovíček
- Lidia Angeleri Hugel
- Jan Trlifaj
- David Pospíšil
- Apostolos Beligiannis
- Chrysostomos Psaroudakis
- Xiao-Wu Chen
- James Gillespie
In Statistical and Nonlinear Physics
- J. Št’ovíček
- Lidia Angeleri Hugel
- David Pospíšil
- Apostolos Beligiannis
- Jan Trlifaj
- Xiao-Wu Chen
- Pu Zhang
- Chrysostomos Psaroudakis
Citations in the corpus
- Deconstructibility and the Hill Lemma in Grothendieck categories (2010, methodology): “[4, 19]), to build up theory for approximations and cotorsion pairs [19], which was among others successfully applied to solve the Baer splitting problem [3] and to prove finite type of tilting modules [5,6].”
- Tilting, cotilting, and spectra of commutative noetherian rings (2012, methodology): “Using results from [2,7,8], we learn that resolving subclasses of mod–R parametrize tilting classes (and hence also the tilting modules up to equivalence):”
- On algebras of finite Cohen-Macaulay type (2011, background): “Then pX, Tq is a cotorsion pair of finite type in Mod-Λ, where X “ pTq, see [20].”