Apparaît dans la collection : 2018 - T1 - WS2 - Model theory and valued fields

A study of those valuations based, in the case where the domain is complete, on the relations between the elements of a minimal system of generators of the value semigroup or of the associated graded algebra. The main idea is to present the ring as a quotient of a generalized power series ring instead of trying to present it `a la Kaplansky as a subring of a generalized ring of Puiseux series. The talk will emphasize the description of the valuation rings of Abhyankar valuations and the approximation of non-Abhyankar valuations by Abhyankar semivaluations.