The obstruction to excision in K-theory and in cyclic homology

• 成果类型: Article
• 署名作者: Cortiñas, G
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0473-9
• 发表日期: 2006
• 页码: 143-173
• 关键词: cohomology

摘要

Let f : A -> B be a ring homomorphism of not necessarily unital rings and I Delta A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K-*(A : I). K-*(B:f(I)) to be an isomorphism; it is measured by the birelative groups K-*(A,B:I). Similarly the groups HN*(A,B:I) measure the obstruction to excision in negative cyclic homology. We show that the rational Jones-Goodwillie Chern character induces an isomorphism ch(*): K-*( A,B:I) circle times Q HN*(A circle times Q, B circle times : I circle times Q).