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TITRE / TITLE
Trees, fixed-points and the Cremona group

R脡SUM脡 / ABSTRACT

An action of a group on a space is called decent if every finitely generated subgroup all of whose elements have fixed-points has a global fixed-point. An example is the automorphism group of a tree or a finite product of trees. I will give a sufficient condition for a group acting on a restricted infinite product of trees to be decent. This allows to prove that every finitely generated subgroup of the Cremona group of P^2 all of whose elements are algebraic is bounded. Joint work with Anne Lonjou and Christian Urech.

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