The Gabriel-Roiter filtration of the Ziegler spectrum
Henning Krause, Mike Prest
TL;DR
This paper introduces a Gabriel-Roiter filtration of the Ziegler spectrum for modules over Artin algebras, revealing new structural insights and compactness properties of subcategories of finitely presented modules.
Contribution
It constructs a novel filtration of the Ziegler spectrum indexed by Gabriel-Roiter measures and establishes a compactness result for certain subcategories.
Findings
Filtration of the Ziegler spectrum indexed by Gabriel-Roiter measures
Inclusion preserving maps from modules to posets are studied
A compactness theorem for subcategories of finitely presented modules
Abstract
Inclusion preserving maps from modules over an Artin algebra to complete partially ordered sets are studied. This yields a filtration of the Ziegler spectrum which is indexed by all Gabriel-Roiter measures. Another application is a compactness result for the set of subcategories of finitely presented modules that are closed under submodules.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology