\contentsline {section}{\tocsection {}{}{Introduction}}{1}
\contentsline {section}{\tocsection {}{1}{Geometry, heights}}{4}
\contentsline {section}{\tocsection {}{2}{The local Fourier transform at the trivial character}}{5}
\contentsline {subsection}{\tocsubsection {}{2.1}{Decomposition of the domain}}{5}
\contentsline {subsection}{\tocsubsection {}{2.2}{Volumes}}{6}
\contentsline {section}{\tocsection {}{3}{The local Fourier transform at a non-trivial character}}{8}
\contentsline {section}{\tocsection {}{4}{The height zeta function}}{11}
\contentsline {section}{\tocsection {}{}{References}}{14}