Lifting Artin–Schreier covers with maximal wild monodromy

Let k be an algebraically closed field of characteristic p > 0. We consider the problem of lifting p -cyclic covers of P k 1 as p -cyclic covers C of the projective line over some discrete valuation field K under the condition that the wild monodromy is maximal. We answer positively the problem for covers birationally given by w p − w = t R ( t ) for any additive polynomial R ( t ). One gives further informations about the ramification filtration of the monodromy extension and in the case when p = 2, one computes the conductor exponent f (Jac( C )/ K ) and the Swan conductor sw(Jac( C )/ K ).