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 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 ring of Witt vectors over $\mathbb{F}_p$) In other words, does the operation of taking the field of fractions of the ring of Witt vectors commute with the operation of taking the algebraic closure?