\select@language {french}
\contentsline {section}{\tocsection {}{1}{Langage fonctoriel}}{1}
\contentsline {subsection}{\tocsubsection {}{1.1}{Cat\'egories et foncteurs}}{1}
\contentsline {subsection}{\tocsubsection {}{1.2}{Foncteurs repr\'esentables}}{6}
\contentsline {section}{\tocsection {}{2}{Groupes alg\'ebriques affines}}{11}
\contentsline {subsection}{\tocsubsection {}{2.1}{D\'efinition et exemples}}{11}
\contentsline {subsection}{\tocsubsection {}{2.2}{Big\`ebres}}{14}
\contentsline {subsection}{\tocsubsection {}{2.3}{Constructions \'el\'ementaires}}{21}
\contentsline {subsection}{\tocsubsection {}{2.4}{Changement du corps de base}}{26}
\contentsline {section}{\tocsection {}{3}{Repr\'esentations lin\'eaires}}{29}
\contentsline {subsection}{\tocsubsection {}{3.1}{G\'en\'eralit\'es}}{29}
\contentsline {subsection}{\tocsubsection {}{3.2}{Repr\'esentation r\'eguli\`ere}}{36}
\contentsline {subsection}{\tocsubsection {}{3.3}{Le th\'eor\`eme de Chevalley}}{37}
\contentsline {section}{\tocsection {}{4}{D\'ecomposition de Jordan}}{41}
\contentsline {subsection}{\tocsubsection {}{4.1}{Introduction}}{41}
\contentsline {subsection}{\tocsubsection {}{4.2}{\'El\'ements unipotents}}{43}
\contentsline {subsection}{\tocsubsection {}{4.3}{Groupes diagonalisables et \'el\'ements semi-simples}}{45}
\contentsline {subsection}{\tocsubsection {}{4.4}{D\'ecomposition de Jordan}}{51}
\contentsline {section}{\tocsection {}{5}{Groupes alg\'ebriques et vari\'et\'es alg\'ebriques}}{52}
\contentsline {subsection}{\tocsubsection {}{5.1}{Groupes alg\'ebriques et groupes de matrices}}{53}
\contentsline {subsection}{\tocsubsection {}{5.2}{La vari\'et\'e d'un groupe alg\'ebrique}}{60}
\contentsline {subsection}{\tocsubsection {}{5.3}{Connexit\'e}}{63}
\contentsline {subsection}{\tocsubsection {}{5.4}{Exemples}}{66}
\contentsline {section}{\tocsection {}{6}{Groupes r\'esolubles et groupes unipotents}}{70}
\contentsline {subsection}{\tocsubsection {}{6.1}{Groupes alg\'ebriques r\'esolubles}}{70}
\contentsline {subsection}{\tocsubsection {}{6.2}{Groupes alg\'ebriques unipotents}}{72}
\contentsline {section}{\tocsection {}{}{Appendice : notions d'alg\`ebre commutative et de g\'eom\'etrie alg\'ebrique}}{75}
\contentsline {subsection}{\tocsubsection {}{}{1. D\'efinitions g\'en\'erales}}{75}
\contentsline {subsection}{\tocsubsection {}{}{2. Produit tensoriel}}{76}
\contentsline {subsection}{\tocsubsection {}{}{3. Alg\`ebres de type fini sur un corps}}{78}