Λεπτομέρειες βιβλιογραφικής εγγραφής
| 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] |
| Βάση Δεδομένων: |
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