show/hide this revision's text 2 added 22 characters in body; edited title; added 11 characters in body

Ring of Witt ring vectors and p-adics

This is probably an easy question, but I'm not able to figure it out.

Are the following the same:

  1. Field of fractions of the Witt ring of Witt vectors over the algebraic closure of $\mathbb{F}_p$

  2. Algebraic closure of the field of p-adics (which is the field of fractions of the Witt ring of Witt vectors over $\mathbb{F}_p$)

In other words, does the operation of taking the field of fractions of the Witt ring of Witt vectors commute with the operation of taking the algebraic closure?
show/hide this revision's text 1

Witt ring and p-adics

This is probably an easy question, but I'm not able to figure it out.

Are the following the same:

  1. Field of fractions of the Witt ring over the algebraic closure of $\mathbb{F}_p$

  2. Algebraic closure of the field of p-adics (which is the field of fractions of the Witt ring over $\mathbb{F}_p$)

In other words, does the operation of taking the field of fractions of the Witt ring commute with the operation of taking the algebraic closure?