关于对偶对的相对导出范畴

doi:10.6040/j.issn.1671-9352.0.2021.506

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 23-30.doi: 10.6040/j.issn.1671-9352.0.2021.506

• • 上一篇

关于对偶对的相对导出范畴

刘妍平

西北师范大学经济学院, 甘肃兰州 730070

发布日期:2022-01-07
作者简介:刘妍平(1989— ),女,博士,副教授,研究方向为环的同调理论. E-mail:xbsdlyp@163.com
基金资助:
国家自然科学基金资助项目(11861055);甘肃省教育厅创新基金项目(2021A-002)

Relative derived category with respect to a duality pair

LIU Yan-ping

College of Economics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2022-01-07

摘要/Abstract

摘要： 研究关于(L,A)- Gorenstein投射模和(L,A)- Gorenstein内射模的相对导出范畴,其中(L,A)是一给定的完备对偶对,得到了相对导出范畴的三角等价和相对导出范畴的态射刻画。同时讨论了一类广义Tate上同调及其性质,得到了Avramov-Martsinkovsky型正合序列。

关键词: 对偶对, 相对导出范畴, Tate上同调, Avramov-Martsinkovsky型正合序列

Abstract: The relative derived categories with respect to Gorenstein(L,A)-projective and Gorenstein(L,A)-injective modules are introduced, where(L,A)is a fixed complete duality pair. A triangle-equivalence and description of morphisms in such relative derived categories are given. We also discuss a generalized Tate cohomology and obtain Avramov-Martsinkovsky exact sequences.

Key words: duality pair, relative derived category, Tate cohomology, Avramov-Martsinkovsky exact sequence

中图分类号:

O153.3

刘妍平. 关于对偶对的相对导出范畴[J]. 《山东大学学报(理学版)》, 2022, 57(2): 23-30.

LIU Yan-ping. Relative derived category with respect to a duality pair[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 23-30.

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关于对偶对的相对导出范畴

Relative derived category with respect to a duality pair

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