Unveiling the Abelian Spectrum of Triangulated Categories Article Swipe
Revista, Zen
,
MATH, 10
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17833372
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17833372
In this paper, we delve into the intricate structure of triangulated categories, focusing on the construction and properties of their Abelian spectrum. We introduce a novel approach to understanding the local behavior of these categories by associating them with a space of Abelian subcategories. This spectrum, equipped with a suitable topology, provides a powerful tool for classifying and studying triangulated categories. Our investigation explores the relationships between the Abelian spectrum and other invariants, such as the Balmer spectrum, and examines applications to representation theory and algebraic geometry. We present new results concerning the structure of the Abelian spectrum for specific classes of triangulated categories, including derived categories of algebras and stable homotopy categories. The overarching goal is to establish the Abelian spectrum as a fundamental invariant that captures essential information about the triangulated structure.
Related Topics
Concepts
Abelian group
Mathematics
Triangulated category
Spectrum (functional analysis)
Abelian category
Pure mathematics
Invariant (physics)
Algebra over a field
Derived category
Representation (politics)
Algebraic structure
Homotopy
Space (punctuation)
Homological algebra
Equivalence of categories
Algebraic number
Homotopy category
Triangulation
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17833372
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7108906215
All OpenAlex metadata
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https://openalex.org/W7108906215Canonical identifier for this work in OpenAlex
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https://doi.org/10.5281/zenodo.17833372Digital Object Identifier
- Title
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Unveiling the Abelian Spectrum of Triangulated CategoriesWork title
- Type
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articleOpenAlex work type
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2025Year of publication
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2025-12-05Full publication date if available
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Revista, Zen, MATH, 10List of authors in order
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https://doi.org/10.5281/zenodo.17833372Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://doi.org/10.5281/zenodo.17833372Direct OA link when available
- Concepts
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Abelian group, Mathematics, Triangulated category, Spectrum (functional analysis), Abelian category, Pure mathematics, Invariant (physics), Algebra over a field, Derived category, Representation (politics), Algebraic structure, Homotopy, Space (punctuation), Homological algebra, Equivalence of categories, Algebraic number, Homotopy category, TriangulationTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
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