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.

Full text: dvi.gz 78 k, dvi 210 k, ps.gz 358 k, pdf 341 k.

Home Page of DOCUMENTA MATHEMATICA