All Questions

I've been thinking about the geometry of inseparable field extensions lately, since I'm studying smoothness in commutative rings in an advanced topics course this semester. I've generally come to the ...

Let $k$ be a field of characteristic $p>0$ (not necessarily perfect). Consider the Frobenius endomorphism $F : k \to k$, $x \mapsto x^p$. I am curious about what happens when we take $k$ as a $k$-...

Is there any known example of a perfect pseudo algebraically closed field of positive characteristic containing $\overline{\mathbb{F}_p}$ but is not algebraically closed?