Skip to main content
MathOverflow

Return to Question

improved formatting
Source Link
edit approved May 30, 2014 at 21:26
Community Bot
edit approved May 30, 2014 at 21:26
Community Bot
  • 1
  • 2
  • 3

Let $(R, m)$ be noetherian local, $dim$\dim(R)=1$,. Show $CH^1(R)=\mathbb{Z}/(gcd\gcd([k_i, R/m]))$, where $k_i$ are residue fields of normalization

Let $R$ be a $1$-dimensional noetherian local domain. Then we have that $CH^1(R)=\mathbb{Z}/(\gcd([k_i, k]))$ where the $k_i$ are residue fields of the normalization and $k$ is the residue field of $R$.

Let $R$ be a $1$-dimensional noetherian local domain, then we have that $CH^1(R)=\mathbb{Z}/(gcd([k_i, k]))$ where the $k_i$ are residue fields of the normalization and $k$ is the residue field of $R$. This was noted in a book, but cannot figure out how to prove, or where it comes from. If anyone could give or sketch a proof, I would be much obliged.

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

Let $R$ be a $1$-dimensional noetherian local domain, then we have that $CH^1(R)=\mathbb{Z}/(gcd([k_i, k]))$ where the $k_i$ are residue fields of the normalization and $k$ is the residue field of $R$. This was noted in a book, but cannot figure out how to prove, or where it comes from. If anyone could give or sketch a proof, I would be much obliged.

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

Let $R$ be a $1$-dimensional noetherian local domain. Then we have that $CH^1(R)=\mathbb{Z}/(\gcd([k_i, k]))$ where the $k_i$ are residue fields of the normalization and $k$ is the residue field of $R$.

This was noted in a book, but cannot figure out how to prove, or where it comes from. If anyone could give or sketch a proof, I would be much obliged.

Source Link
Pax
Pax
  • 841
  • 6
  • 16

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

Let $R$ be a $1$-dimensional noetherian local domain, then we have that $CH^1(R)=\mathbb{Z}/(gcd([k_i, k]))$ where the $k_i$ are residue fields of the normalization and $k$ is the residue field of $R$. This was noted in a book, but cannot figure out how to prove, or where it comes from. If anyone could give or sketch a proof, I would be much obliged.