Upper ramification sequences of nonabelian extensions of degree $p^3$ in characteristic $p$

Abstract

We classify the upper ramification breaks of totally ramified nonabelian extensions of degree $p^3$ over a local field of characteristic $p>0$. We find that nonintegral upper ramification breaks can occur for each nonabelian Galois group of order $p^3$, except the dihedral group of order $8$.

arXiv comment20 pages