On the exactness of products in the localization of (Ab.4*) Grothendieck categories

被引：0

作者：

Virili, Simone ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, Via Trieste 63, I-35121 Padua, Italy

来源：

JOURNAL OF ALGEBRA | 2017年 / 470卷

关键词：

Grothendieck categories; Gabriel dimension; Injective classes; Torsion theories; Local cohomology; Derived category; LOCAL CO-HOMOLOGY; FUNCTORS; LIMITS;

D O I：

10.1016/j.jalgebra.2016.08.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let C be an (Ab.4*) Grothendieck category, that is, products are exact in C. Given a hereditary torsion class T subset of C, we study the exactness of products in the Gabriel localization C/T of C. We show that, under suitable assumptions on C, the k + 1-th derived functor of the product vanishes, provided the Gabriel dimension of C/T is smaller than k. As a consequence, we deduce that, under suitable hypotheses, the derived category D(C/T) is left-complete. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：37 / 67

页数：31

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