Timeline for Let $(R, m)$ be noetherian local, $\dim(R)=1$. Show $CH^1(R)=\mathbb{Z}/(\gcd([k_i, R/m]))$, where $k_i$ are residue fields of normalization
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| S May 30, 2014 at 21:26 | history | suggested | CommunityBot | CC BY-SA 3.0 |
improved formatting
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| May 30, 2014 at 21:13 | review | Suggested edits | |||
| S May 30, 2014 at 21:26 | |||||
| May 14, 2014 at 5:57 | comment | added | naf | This follows more or less from the definitions: Since $R$ is one dimensional and local the group is generated by the class of the unique closed point. The relations are given (as in Fulton's book) using the normalisation which is a PID (since it is one dimensional normal and semi-local, assuming perhaps that the normalisation is finite). The image in $CH^1(R)$ of the class of a closed point in the normalisation is given by $[k_i:k]$ times the generator where $k_i$ is the corresponding reside field. | |
| May 13, 2014 at 23:58 | comment | added | Steven Landsburg | What book? ${}{}{}{}{}{}{}{}{}{}{}{}$ | |
| May 13, 2014 at 21:36 | history | asked | Pax | CC BY-SA 3.0 |