The Equivalence of Two Notions of Discreteness of Triangulated Categories

被引：0
作者：
Lingling Yao
Dong Yang
机构：
[1] Southeast University,School of Mathematics
[2] Nanjing University,Department of Mathematics
来源：
Algebras and Representation Theory | 2021年 / 24卷
关键词：
Derived discrete; Discreteness of triangulated category; ST-triple; T-structure; Co-t-structure; 18E30; 16E35;
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学科分类号：
摘要：
Given an ST-triple (C,D,M)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\mathcal {C},\mathcal {D},M)$\end{document} one can associate a co-t-structure on C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {C}$\end{document} and a t-structure on D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {D}$\end{document}. It is shown that the discreteness of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {C}$\end{document} with respect to the co-t-structure is equivalent to the discreteness of D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {D}$\end{document} with respect to the t-structure. As a special case, the discreteness of Db(modA)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {D}^{b}(\textsf {mod} A)$\end{document} in the sense of Vossieck is equivalent to the discreteness of Kb(projA) in a dual sense, where A is a finite-dimensional algebra.
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页码：1295 / 1312
页数：17
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