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3 results

  • Automorphisms of Drinfeld half-spaces over a finite field

  • Part of
  • Bertrand Rémy, Amaury Thuillier, Annette Werner
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 7 / July 2013
    Published online by Cambridge University Press:
    26 April 2013, pp. 1211-1224
    Print publication:
    July 2013
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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.

  • Sur les automorphismes du groupe de Cremona

  • Julie Déserti
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 6 / November 2006
    Published online by Cambridge University Press:
    24 November 2006, pp. 1459-1478
    Print publication:
    November 2006
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  • We prove that an automorphism of the group of birational transformations of the complex projective plane is the composition of an interior automorphism and an automorphism of the field $\mathbb{C}$. The proof is based on a study of maximal abelian subgroups of the Cremona group.