Equality of Two Non-Logarithmic Ramification Filtrations of Abelianized Galois Group in Positive Characteristic
We prove the equality of two non-logarithmic ramification filtrations defined by Matsuda and Abbes-Saito of the abelianized absolute Galois group of a complete discrete valuation field in positive characteristic. We compute the refined Swan conductor and the characteristic form of a character of the fundamental group of a smooth separated scheme over a perfect field of positive characteristic by using sheaves of Witt vectors.
2010 Mathematics Subject Classification: primary 11S15, secondary 14G22
Keywords and Phrases: local field, ramification filtration, characteristic form, Witt vector.
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