\BOOKMARK [1]{section.2}{Classes of functions}{}
\BOOKMARK [2]{subsection.2.1}{Notations}{section.2}
\BOOKMARK [2]{subsection.2.2}{Definitions}{section.2}
\BOOKMARK [2]{subsection.2.3}{First properties}{section.2}
\BOOKMARK [2]{subsection.2.4}{Orders}{section.2}
\BOOKMARK [2]{subsection.2.5}{Rank 2 case}{section.2}
\BOOKMARK [2]{subsection.2.6}{Rank 3 case}{section.2}
\BOOKMARK [2]{subsection.2.7}{Exceptional lattices}{section.2}
\BOOKMARK [2]{subsection.2.8}{Rank 3 case: A0}{section.2}
\BOOKMARK [1]{section.3}{Reductions}{}
\BOOKMARK [2]{subsection.3.1}{Reduction of S}{section.3}
\BOOKMARK [2]{subsection.3.2}{Reduction of the rank}{section.3}
\BOOKMARK [2]{subsection.3.3}{The exceptional case}{section.3}
\BOOKMARK [2]{subsection.3.4}{Checking the AF-property}{section.3}
\BOOKMARK [1]{section.4}{AF-functions and geometry}{}
\BOOKMARK [2]{subsection.4.1}{Affine geometry}{section.4}
\BOOKMARK [2]{subsection.4.2}{Projective geometry}{section.4}
\BOOKMARK [2]{subsection.4.3}{Logarithmic functions}{section.4}
\BOOKMARK [2]{subsection.4.4}{Existence of AF-functions}{section.4}
\BOOKMARK [1]{section.5}{Galois theory}{}
\BOOKMARK [2]{subsection.5.1}{Groups}{section.5}
\BOOKMARK [2]{subsection.5.2}{Fields}{section.5}
\BOOKMARK [2]{subsection.5.3}{Galois groups}{section.5}
\BOOKMARK [2]{subsection.5.4}{Commuting pairs}{section.5}
\BOOKMARK [1]{section.6}{Valuations}{}
\BOOKMARK [2]{subsection.6.1}{Notations}{section.6}
\BOOKMARK [2]{subsection.6.2}{Inertia group}{section.6}
\BOOKMARK [2]{subsection.6.3}{Valuations and flag functions}{section.6}
\BOOKMARK [2]{subsection.6.4}{AF-functions on a}{section.6}