Corpus ID: 235694634

Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups

@inproceedings{ArenasCarmona2021QuotientsOT,
  title={Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups},
  author={Luis Arenas-Carmona and Claudio Bravo and Beno{\^i}t Loisel and Giancarlo Lucchini Arteche},
  year={2021}
}
Let K be the function field of a curve C over a field F of either odd or zero characteristic. Following the work by Serre and Mason on SL2, we study the action of arithmetic subgroups of SU(3) on its corresponding Bruhat-Tits tree associated to a suitable completion of K. More precisely, we prove that the quotient graph “looks like a spider”, in the sense that it is the union of a set of cuspidal rays (the “legs”), parametrized by an explicit Picard group, that are attached to a connected graph… Expand

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References

SHOWING 1-10 OF 16 REFERENCES
Computing quaternion quotient graphs via representations of orders
Abstract We give a method to describe the quotient of the local Bruhat–Tits tree T P for PGL 2 ( K ) , where K is a global function field, by certain subgroups of PGL 2 ( K ) of arithmeticalExpand
Serre’s generalization of Nagao’s theorem: An elementary approach
Let C be a smooth projective curve over a field k. For each closed point Q of C let C = C(C,Q, k) be the coordinate ring of the affine curve obtained by removing Q from C. Serre has proved thatExpand
Application of the Bruhat-Tits tree of SU3( h) to some Ã2 groups
Let K be a nonarchimedean local field, let L be a separable quadratic extension of K , and let h denote a nondegenerate sesquilinear formk on L 3 . The Bruhat-Tits building associated with SU 3 ( h )Expand
Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: the Rank Theorem
We show that the niteness length of an S-arithmetic subgroup in a noncommutative isotropic absolutely almost simple groupG over a global function eld is one less than the sum of the local ranks of GExpand
Strong approximation for semi-simple groups over function fields
Let K be a field and A be a K-algebra. For a variety V, defined over K, we shall let V(A) denote the set of A-rational points of V. In case A is a locally compact topological ring, V(A) has a naturalExpand
Lattices in rank one Lie groups over local fields
AbstractWe prove that if $$G = \underline G (K)$$ is theK-rational points of aK-rank one semisimple group $$\underline G $$ over a non archimedean local fieldK, thenG has cocompact non-arithmeticExpand
The structure of the group G(k[t]): Variations on a theme of Soulé
Following Soule’s ideas [14] we give a presentation of the abstract group G(k[t]) for any semisimple (connected) simply connected absolutely almost simple k–group G. As an application, we give aExpand
Algebraic function fields and codes
TLDR
This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded and contains numerous exercises that help the reader to understand the basic material. Expand
A Compactification of the Bruhat-Tits Building
The apartment.- The o K -group schemes in the quasi-split case.- The building in the quasi-split case.- The building and its compactification.
Groupes réductifs sur un corps local
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