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%\date{} % Activate to display a given date or no date  \begin{document}  The localization Theorem and the Gersten conjecture ofen often  reduce general problems of Algebraic-K theory to the particular case of fields. The aim of the seminar will be understand the $K$-theory of fields, we will recall some of the constructions of the higher $K$-groups and achieved by Quillen and its basic properties as Localization theorem, Gersten's conjecture Projective Bundle Formula; but instead in focus in the theoretical proofs we will study explicit computations around the $K$-theory fields. One of the aims is study the proof of one of the Qullien-Lichtenbaum conjectures:  \begin{theo}