A local ring such that the map between Grothendieck groups with rational coefficient induced by completion is not injective

2007/07/04 by Kurano, Kazuhiko, Srinivas, Vasudevan · 1 citation
#13D15 #19A49 #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.0707.0547

Abstract

In this paper, we construct a local ring A such that the kernel of the map G₀(A)\subq → G₀(A)\subq is not zero, where A is the comletion of A with respect to the maximal ideal, and G₀()\subq is the Grothendieck group of finitely generated modules with rational coefficient. In our example, A is a two-dimensional local ring which is essentially of finite type over \Bbb C, but it is not normal.

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• Grothendieck groups and completions of Gorenstein local rings

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