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Automorphisms of Drinfeld half-spaces over a finite field

Part of: Birational geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  26 April 2013

Bertrand Rémy ,
Amaury Thuillier  and
Annette Werner
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

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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.

Keywords

)14G22, 14G15, 14E05 (primarynon-Archimedean analytic geometryBerkovich spacesDrinfeld upper half-spacebirational transformations

MSC classification

Secondary: 14G22: Rigid analytic geometry 14G15: Finite ground fields 14E05: Rational and birational maps
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 7 , July 2013 , pp. 1211 - 1224
Copyright
© The Author(s) 2013 

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