Immeubles affines et groupes de Kac-Moody

Abstract : This work aims at generalizing Bruhat-Tits theory to Kac-Moody groups over local fields. We thus try to construct a geometric space on wich such a group will act, and wich will look like the Bruhat-Tits building of a reductive group. Actually, the first part stays in the field of Bruhat-Tits theory as it exposes a family of compactification of an ordinary affine building. It is in the second part that we move to Kac-Moody theory, using the first part as a guide. The spaces obtained do not satisfy all the requirement for a building, as two points are not always in one apartment. They will be called hovels ("masures" in french), and more precisly bounded hovels.
Document type :
Mathematics. université Henri Poincarré nancy 1, 2010. French
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Contributor : Cyril Charignon <>
Submitted on : Tuesday, July 6, 2010 - 11:47:01 AM
Last modification on : Tuesday, October 5, 2010 - 10:32:46 AM


  • HAL Id : tel-00497961, version 1



Cyril Charignon. Immeubles affines et groupes de Kac-Moody. Mathematics. université Henri Poincarré nancy 1, 2010. French. <tel-00497961>




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