Ramification of cyclic extensions of degree $p^2$ of complete discrete valuation fields of prime characteristic $p$ with imperfect residue field

In the present paper we study ramification invariants of complete discrete valuation fields of prime characteristic $p$ with imperfect residue field. Using Witt vectors we calculate ramification breaks of cyclic extensions of degree $p^2$ of such field. We obtain necessary and sufficient conditions for a pair of natural numbers to be ramification breaks of a cyclic extension of degree $p^2$.