| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Algebraic Geometry
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| Title: |
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Automorphisms of Drinfeld half-spaces over a finite field |
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| Author(s): |
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Bertrand RÉMY 1, Amaury Thuillier 1, Annette Werner 2 |
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| Laboratory: |
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| 1: |
Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX |
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France |
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| 2: |
Institut für Mathematik |
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Goethe-Universität Frankfurt |
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Robert-Maier-Str., 6-8 D-60325 Frankfurt-am-Main |
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Germany |
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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. |
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| Fulltext language: |
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English |
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| Production date: |
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2012-06-01 |
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| Keyword(s): |
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Non-archimedean analytic geometry – Berkovich spaces – Drinfeld upper half-space – birational transformations |
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| Classification: |
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14G22, 14G15, 14E05 |
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