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

August, Jenny

doi:10.1007/s00209-020-02475-y

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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アイテムのパーマリンク: https://hdl.handle.net/21.11116/0000-0006-9C32-2 版のパーマリンク: https://hdl.handle.net/21.11116/0000-0009-CEDA-A

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August, Jenny¹, 著者

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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201

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キーワード: Mathematics, Representation Theory, Algebraic Geometry

要旨: 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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言語: eng - English

日付: 出版: 2020

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識別子（DOI, ISBNなど）: arXiv: 1801.05687
DOI: 10.1007/s00209-020-02475-y
URI: http://arxiv.org/abs/1801.05687

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出版物名: Mathematische Zeitschrift

省略形 : Math. Z.

種別: 学術雑誌

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出版社, 出版地: Springer

ページ: - 巻号: 296 (3-4) 通巻号: - 開始・終了ページ: 1157 - 1183 識別子（ISBN, ISSN, DOIなど）: -

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