Event
Finiteness properties of S-arithmetic groups in positive characteristic| Title of the event | Finiteness properties of S-arithmetic groups in positive characteristic |
| Series | MathematischeGesellschaft |
| Organizer | Mathematisches Institut |
| Speaker | Prof. Dr. Ralf Köhl |
| Speaker institution | Justus-Liebig-Universität Gießen |
| Type of event | Kolloquium |
| Category | Forschung |
| Registration required | Nein |
| Details | The finiteness properties of discrete groups measure whether a given group is finitely generated, finitely presented or, more generally, admits an Eilenberg-MacLane space with a finite n-skeleton. By a result by Borel-Serre, S-arithmetic groups in characteristic 0 enjoy the above finiteness properties for any given natural number n. In contrast, the group SL(2,F_q[t]) -- and more generally, any non-uniform tree lattice -- is not even finitely generated. In 2013, Bux, Witzel, and myself established these finiteness properties in positive characteristic based on filtrations of Bruhat-Tits buildings via Busemann functions stemming from Harder's reduction theory. In my talk I will revise the above-mentioned finiteness properties, establish the non-finite generation of tree lattices, discuss the relationship between the geometry of numbers in positive characteristic and the Riemann-Roch theorem, and then introduce the Busemann functions coming from Harder's reduction theory. |
| Date | Start: 27.06.2019, 16:15 Uhr Ende: 27.06.2019 , 17:15 Uhr |
| Location |
Mathematisches Institut (Bunsenstr 3-5) Sitzungszimmer |
| Contact |
0551-3927752 annalena.wendehorst@mathematik.uni-goettingen.de |