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  On the finiteness of the derived equivalence classes of some stable endomorphism rings

August, J. (2020). On the finiteness of the derived equivalence classes of some stable endomorphism rings. Mathematische Zeitschrift, 296(3-4), 1157-1183. doi:10.1007/s00209-020-02475-y.

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Datensatz-Permalink: https://hdl.handle.net/21.11116/0000-0006-9C32-2 Versions-Permalink: https://hdl.handle.net/21.11116/0000-0009-CEDA-A
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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 Urheber:
August, Jenny1, Autor           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Schlagwörter: Mathematics, Representation Theory, Algebraic Geometry
 Zusammenfassung: We prove that the stable endomorphism rings of rigid objects in a suitable
Frobenius category have only finitely many basic algebras in their derived
equivalence class and that these are precisely the stable endomorphism rings of
objects obtained by iterated mutation. The main application is to the Homological Minimal Model Programme. For a 3-fold flopping contraction $f \colon X \to \mathrm{Spec}\ R$, where $X$ has only Gorenstein terminal singularities, there is an associated finite dimensional algebra
$A_{\mathrm{con}}$ known as the contraction algebra. As a corollary of our main result, there are only finitely many basic algebras in the derived equivalence
class of $A_{\mathrm{con}}$ and these are precisely the contraction algebras of
maps obtained by a sequence of iterated flops from $f$. This provides evidence
towards a key conjecture in the area.

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Sprache(n): eng - English
 Datum: 2020
 Publikationsstatus: Erschienen
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 Ort, Verlag, Ausgabe: -
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 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: arXiv: 1801.05687
DOI: 10.1007/s00209-020-02475-y
URI: http://arxiv.org/abs/1801.05687
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Titel: Mathematische Zeitschrift
  Kurztitel : Math. Z.
Genre der Quelle: Zeitschrift
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Ort, Verlag, Ausgabe: Springer
Seiten: - Band / Heft: 296 (3-4) Artikelnummer: - Start- / Endseite: 1157 - 1183 Identifikator: -