If we pute let $\mathbb{F}{q}$ \mathbb{F}_{q}$ be the finite field with$q$elements, is there a local field$F$with residue field $\mathbb{F}{q}$\mathbb{F}_{q}$ ?
If we pute $\mathbb{F}{q}$ the finite field with $q$ elements, is there a local field $F$ with residue field $\mathbb{F}{q}$ ?