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Mutation and the Gabriel spectrum.

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Τίτλος: Mutation and the Gabriel spectrum.
Συγγραφείς: Hrbek, Michal1 (AUTHOR) hrbek@math.cas.cz, Pavon, Sergio2 (AUTHOR) sergio.pavon@univr.it, Vitória, Jorge3 (AUTHOR) jorge.vitoria@unipd.it
Πηγή: Selecta Mathematica, New Series. Apr2026, Vol. 32 Issue 2, p1-58. 58p.
Θεματικοί όροι: *Mutations (Algebra), *Topology, *Triangulated categories, *Noetherian rings, *Abelian categories
Περίληψη: Mutations occur in multiple algebraic contexts, often enjoying good combinatorial properties. In this paper we study mutations of pure-injective cosilting objects in compactly generated triangulated categories from a topological point of view. We consider the topologies studied by Gabriel, Burke and Prest on the set of indecomposable injective objects in a Grothendieck abelian category, transfer them to associated cosilting subcategories, and show that, in that context, right mutation induces a homeomorphism on two complementary subspaces. We then improve this result in the context of the derived category of a commutative noetherian ring, showing that right mutation is an open bijection. We end the paper with a detailed analysis of a range of cosilting subcategories over commutative noetherian rings for which the topology is completely known. As a byproduct of this analysis, we obtain that the category of modules over a commutative noetherian ring is the unique locally noetherian Grothendieck category in its derived-equivalence class. [ABSTRACT FROM AUTHOR]
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  Data: Mutation and the Gabriel spectrum.
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  Data: <searchLink fieldCode="AR" term="%22Hrbek%2C+Michal%22">Hrbek, Michal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hrbek@math.cas.cz</i><br /><searchLink fieldCode="AR" term="%22Pavon%2C+Sergio%22">Pavon, Sergio</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> sergio.pavon@univr.it</i><br /><searchLink fieldCode="AR" term="%22Vitória%2C+Jorge%22">Vitória, Jorge</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> jorge.vitoria@unipd.it</i>
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  Data: <searchLink fieldCode="JN" term="%22Selecta+Mathematica%2C+New+Series%22">Selecta Mathematica, New Series</searchLink>. Apr2026, Vol. 32 Issue 2, p1-58. 58p.
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  Data: *<searchLink fieldCode="DE" term="%22Mutations+%28Algebra%29%22">Mutations (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Topology%22">Topology</searchLink><br />*<searchLink fieldCode="DE" term="%22Triangulated+categories%22">Triangulated categories</searchLink><br />*<searchLink fieldCode="DE" term="%22Noetherian+rings%22">Noetherian rings</searchLink><br />*<searchLink fieldCode="DE" term="%22Abelian+categories%22">Abelian categories</searchLink>
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  Data: Mutations occur in multiple algebraic contexts, often enjoying good combinatorial properties. In this paper we study mutations of pure-injective cosilting objects in compactly generated triangulated categories from a topological point of view. We consider the topologies studied by Gabriel, Burke and Prest on the set of indecomposable injective objects in a Grothendieck abelian category, transfer them to associated cosilting subcategories, and show that, in that context, right mutation induces a homeomorphism on two complementary subspaces. We then improve this result in the context of the derived category of a commutative noetherian ring, showing that right mutation is an open bijection. We end the paper with a detailed analysis of a range of cosilting subcategories over commutative noetherian rings for which the topology is completely known. As a byproduct of this analysis, we obtain that the category of modules over a commutative noetherian ring is the unique locally noetherian Grothendieck category in its derived-equivalence class. [ABSTRACT FROM AUTHOR]
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        Value: 10.1007/s00029-026-01127-z
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        Text: English
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      – SubjectFull: Topology
        Type: general
      – SubjectFull: Triangulated categories
        Type: general
      – SubjectFull: Noetherian rings
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      – SubjectFull: Abelian categories
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      – TitleFull: Mutation and the Gabriel spectrum.
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            NameFull: Hrbek, Michal
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              Text: Apr2026
              Type: published
              Y: 2026
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