On maps of Grothendieck groups induced by completion

✍ Scribed by Yuji Kamoi; Kazuhiko Kurano

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 188 KB
• Volume: 254
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00082-0

✦ Synopsis

We prove that the induced map G 0 (A) → G 0 ( A ) by completion is injective if A is an excellent noetherian local ring that satisfies one of the following three conditions: (i) A is henselian; (ii) A is a local ring at the homogeneous maximal ideal of a homogeneous ring over a field; (iii) A has at most isolated singularity.