The acyclicity of the Frobenius functor for modules of finite flat dimension

被引：4

作者：

Marley, Thomas ^{[1
]}

Webb, Marcus ^{[2
]}

机构：

[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[2] Stephen F Austin State Univ, Dept Math & Stat, Nacogdoches, TX 75962 USA

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2016年 / 220卷 / 08期

关键词：

COVERS; RINGS;

D O I：

10.1016/j.jpaa.2016.01.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a commutative Noetherian local ring of prime characteristic p and f : R -> R the Frobenius ring homomorphism. For e >= 1 let R-(e) denote the ring R viewed as an R-module via f(e). Results of Peskine, Szpiro, and Herzog state that for finitely generated modules M, M has finite projective dimension if and only if Tor(i)(R)(R-(e), M) = 0 for all i > 0 and all (equivalently, infinitely many) e >= 1. We prove this statement holds for arbitrary modules using the theory of flat covers and minimal flat resolutions. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：2886 / 2896

页数：11

共 18 条

[1]

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