Revista Matemática Iberoamericana

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Volume 19, Issue 2, 2003, pp. 467–482
DOI: 10.4171/RMI/358

Published online: 2003-08-31

Valuations in fields of power series

Francisco Javier Herrera Govantes[1], Miguel Ángel Olalla Acosta[2] and José Luis Vicente Córdoba[3]

(1) Universidad de Sevilla, Spain
(2) Universidad de Sevilla, Spain
(3) Universidad de Sevilla, Spain

This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of power series in two and three variables, according to their residue fields. We prove that all our cases are possible and give explicit constructions.

Keywords: Valuation theory, power series

Herrera Govantes Francisco Javier, Olalla Acosta Miguel Ángel, Vicente Córdoba José Luis: Valuations in fields of power series. Rev. Mat. Iberoam. 19 (2003), 467-482. doi: 10.4171/RMI/358