Invitation to higher local fields, Part I, section 18: On ramification theory of monogenic extensions

Invitation to higher local fields, Part I, section 17: An approach to higher ramification theory

This is an introduction to author's ramification theory of a complete discrete valuation field with residue field whose p-basis consists of at most one element. New lower and upper filtrations are defined; cyclic extensions of degree p may have non-integer ramification breaks. A refinement of the filtration for two-dimensional local fields which is compatible with the reciprocity map is discussed.