K'-Theory of a Local Ring of Finite Cohen-Macaulay Type

2011/08/09 by Viraj Navkal, Navkal, Viraj
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.AC #math.AG #math.KT #msc:13D15 #msc:16E20 #msc:19D50

paper · pdf · doi:10.48550/arxiv.1108.2000

20 pages; significant corrections and additions to original version

arxiv created 2012/08/28 · arxiv updated 2012/08/29

Abstract

We study the K'-theory of a CM Henselian local ring R of finite Cohen-Macaulay type. We first describe a long exact sequence involving the groups K_i'(R) and the K-groups of certain other rings, including the Auslander algebra. By examining the terms and maps in the sequence, we obtain information about K'(R).

Related

• K-groups for rings of finite Cohen-Macaulay type
• Local rings of bounded Cohen-Macaulay type
• Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum
• Test properties of some Cohen-Macaulay modules and criteria for local rings via finite vanishing of (co)homologies
• Local rings of countable Cohen--Macaulay type