Skip to main content
MathOverflow

Return to Question

deleted 1 character in body; edited title
Source Link
Duality
Duality
  • 1.5k
  • 7
  • 13

Local field such that the value group of $K^\text{sepperf}$ (separable perfect closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$

Let $K$ be a local field of positive characteristic. I'm looking for a $K$ which satisfies the following condition.

  • Value group of $K^\text{sep}$$K^\text{perf}$ (separableperfect closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$.

$K$ should be like the form $ \Bbb{F}_q((t))$, so I need to determine $q$.

Local field such that the value group of $K^\text{sep}$ (separable closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$

Let $K$ be a local field of positive characteristic. I'm looking for a $K$ which satisfies the following condition.

  • Value group of $K^\text{sep}$ (separable closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$.

$K$ should be like the form $ \Bbb{F}_q((t))$, so I need to determine $q$.

Local field such that the value group of $K^\text{perf}$ ( perfect closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$

Let $K$ be a local field of positive characteristic. I'm looking for a $K$ which satisfies the following condition.

  • Value group of $K^\text{perf}$ (perfect closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$.

$K$ should be like the form $ \Bbb{F}_q((t))$, so I need to determine $q$.

Proofreading
Source Link
LSpice
LSpice
  • 12.9k
  • 4
  • 45
  • 69

Local field whosesuch that the value group of $K^$K^\text{sep}$  (Separableseparable closure of $K$) is $\bigcup_{n≧1n\geqq1}(1/p^n) \Bbb{Z}$

Let $K$ be a local field of positive characteristic. I'm looking for ana $K$ which satisfies the following condition.

・Value group of $K^{sep}$(Separable closure of $K$) is $\bigcup_{n≧1}(1/p^n) \Bbb{Z}$

  • Value group of $K^\text{sep}$ (separable closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$.

$K$ should be like the form $ \Bbb{F}_q((t))$, so I need to determine $q$.

Local field whose value group of $K^{sep}$(Separable closure of $K$) is $\bigcup_{n≧1}(1/p^n) \Bbb{Z}$

Let $K$ be a local field of positive characteristic. I'm looking for an $K$ which satisfies the following condition.

・Value group of $K^{sep}$(Separable closure of $K$) is $\bigcup_{n≧1}(1/p^n) \Bbb{Z}$

$K$ should be like the form $ \Bbb{F}_q((t))$, so I need to determine $q$.

Local field such that the value group of $K^\text{sep}$  (separable closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$

Let $K$ be a local field of positive characteristic. I'm looking for a $K$ which satisfies the following condition.

  • Value group of $K^\text{sep}$ (separable closure of $K$) is $\bigcup_{n\geqq1}(1/p^n) \Bbb{Z}$.

$K$ should be like the form $ \Bbb{F}_q((t))$, so I need to determine $q$.

Source Link
Duality
Duality
  • 1.5k
  • 7
  • 13

Local field whose value group of $K^{sep}$(Separable closure of $K$) is $\bigcup_{n≧1}(1/p^n) \Bbb{Z}$

Let $K$ be a local field of positive characteristic. I'm looking for an $K$ which satisfies the following condition.

・Value group of $K^{sep}$(Separable closure of $K$) is $\bigcup_{n≧1}(1/p^n) \Bbb{Z}$

$K$ should be like the form $ \Bbb{F}_q((t))$, so I need to determine $q$.