$\Lambda$-buildings associated to quasi-split reductive groups
Benoit Loisel (Université de Poitiers)
- https://www.uni-giessen.de/de/fbz/fb07/fachgebiete/mathe/veranstaltungen/wissenschaftliche_veranstaltungen/oberseminar_algebra_geometrie_topologie/termine/loisel
- $\Lambda$-buildings associated to quasi-split reductive groups
- 2024-10-22T16:00:00+02:00
- 2024-10-22T18:00:00+02:00
- Benoit Loisel (Université de Poitiers)
22.10.2024 von 16:00 bis 18:00 (Europe/Berlin / UTC200)
Hörsaal 111
Abstract: Let $G$ be a reductive group and $K$ be a field with a valuation $\omega$. In 1972 and 1984, Bruhat and Tits associated a combinatorial datum, called a building, to the triple $(G,K,\omega)$ whenever $K$ is complete and Henselian and the values of $\omega$ form a subgroup of the real numbers $\mathbb{R}$.
For an arbitrary totally ordered group $\Lambda$ (typically $\Lambda = \mathbb{Z}^d$), in 1994, independently, Bennett and Parshin generalized the definition of buildings to higher local fields with a valuation in $\Lambda$.
In this talk, I will explain how one can attach, with a suitable action, a $\Lambda$-building to the rational points of a (quasi-)split reductive group over such an higher local field. The method follows the construction of Bruhat and Tits via the parahoric subgroups. This is a joint work with Auguste Hébert and Diego Izquierdo.