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Finiteness properties of S-arithmetic groups in positive characteristic
27.6.2019, 16:15 - 17:15
Speaker:Prof. Dr. Ralf Köhl, Justus-Liebig-Universität Gießen
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
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.
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