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We prove the equality of two non-logarithmic ramification filtrations definedby Matsuda and Abbes-Saito for the abelianized absolute Galois group of acomplete discrete valuation field in positive characteristic. We also computethe refined Swan conductor and the characteristic form of a character of thefundamental group of a smooth separated scheme over a perfect field of positivecharacteristic by using sheaves of Witt vectors.

Equality of two non-logarithmic ramification filtrations of abelianized Galois group in positive characteristic