Exact categories, big Cohen-Macaulay modules and finite representation type

Autor:	Psaroudakis, Chrysostomos, Rump, Wolfgang
Rok vydání:	2020
Předmět:	Mathematics - Representation Theory Mathematics - Commutative Algebra Mathematics - Category Theory Mathematics - Rings and Algebras
Druh dokumentu:	Working Paper
Popis:	One of the first remarkable results in the representation theory of artin algebras, due to Auslander and Ringel-Tachikawa, is the characterization of when an artin algebra is representation-finite. In this paper, we investigate aspects of representation-finiteness in the general context of exact categories in the sense of Quillen. In this framework, we introduce "big objects" and prove an Auslander-type "splitting-big-objects" theorem. Our approach generalises and unifies the known results from the literature. As a further application of our methods, we extend the theorems of Auslander and Ringel-Tachikawa to arbitrary dimension, i.e. we characterise when a Cohen-Macaulay order over a complete regular local ring is of finite representation type. Comment: v2: 30 pages, some misprints corrected, references updated, comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.04419 Zobrazit plný text záznamu View this record from Arxiv