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Automorphisms of Drinfeld half-spaces over a finite field

Published online by Cambridge University Press:  26 April 2013

Bertrand Rémy
Affiliation:
Université de Lyon, Université Lyon1-CNRS, Institut Camille Jordan - UMR5208, 43 bd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France email remy@math.univ-lyon1.fr
Amaury Thuillier
Affiliation:
Université de Lyon, Université Lyon1-CNRS, Institut Camille Jordan - UMR5208, 43 bd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France email thuillier@math.univ-lyon1.fr
Annette Werner
Affiliation:
Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Str. 6–8, D-60325 Frankfurt a.M., Germany email werner@math.uni-frankfurt.de
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Abstract

We show that the automorphism group of Drinfeld’s half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the sense of Berkovich over the finite field equipped with the trivial valuation. We also take into account extensions of the base field.

Type
Research Article
Copyright
© The Author(s) 2013 

References

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