Further Remarks on Local Discriminants

Using Kummer theory for a finite extension K of Q_p(ζ) (where p is a prime number and ζ a primitive p-th ischolar_main of 1), we compute the ramification filtration and the discriminant of an arbitrary elementary abelian p-extension of K. We also develop the analogous Artin-Schreier theory for finite extensions of F_p((π)), where π is transcendental, and derive similar results for their elementary abelian p-extensions.