The obstruction to excision in K-theory and in cyclic homology
The obstruction to excision in K-theory and in cyclic homology
复制标题
K理论和循环同调中对切除的阻碍
DOI：
10.1007/s00222-005-0473-9
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发表时间：
2001
影响因子：
3.1
通讯作者：
Guillermo Cortiñas
中科院分区：
文献类型：
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作者：
Guillermo Cortiñas
设A→ B是一个不一定有单位环的环同态，一个理想通过同构映射到B的一个理想上。K-理论中切除的障碍是相对K-群K *（A：I）→K*（B：f（I））之间的映射不能是同构;它由双相对群K *（A，B：I）度量。类似地，基团HN *（A，B：I）测量在负环状同源性中对切除的阻碍。我们证明了有理Jones-Goodwillie Chern特征标诱导同构$$ch_{*}：K_{*}（A，B：I）\otimes\mathbb{Q}\overset{\sim}{\to}HN_{*}（A\otimes\mathbb {Q}，B\otimes\mathbb{Q}：I\otimes\mathbb {Q}）.$$
Letf:A→Bbe a ring homomorphism of not necessarily unital rings andan ideal which is mapped byfisomorphically to an ideal ofB. The obstruction to excision inK-theory is the failure of the map between relativeK-groupsK*(A:I)→K*(B:f(I)) to be an isomorphism; it is measured by the birelative groupsK*(A,B:I). Similarly the groupsHN*(A,B:I) measure the obstruction to excision in negative cyclic homology. We show that the rational Jones-Goodwillie Chern character induces an isomorphism $$ch_{*}:K_{*}(A,B:I)\otimes\mathbb{Q}\overset{\sim}{\to}HN_{*}(A\otimes\mathbb{Q},B\otimes\mathbb{Q}:I\otimes\mathbb{Q}).$$