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International conference on algebraic geometry, complex analysis and computer algebra
August 7, 2016 12:00–13:00, Koryazhma, Arkhangelsk region, Nothern (Arctic) Federal University named after M. V. Lomonosov, Koryazhma Branch, Lenin's prospekt, d. 9
 


Triangulable subgroups of the Cremona groups

V. L. Popov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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Abstract: The talk is aimed to elaborate on the Bass' Triangulability Problem about unipotent algebraic subgroups of the affine Cremona groups. The following topics are discussed: a triangulability criterion, the existence of non-triangulable connected solvable affine algebraic subgroups of the Cremona groups, and stable triangulability of such subgroups; in particular, in the stable range the Bass' Triangulability Problem is answered in the affirmative. These results are based on a general theorem about invariant subfields of purely transcendental field extensions of transcendental degree 1. A general construction of all rationally triangulable subgroups of the Cremona groups is given, and, as an application, all rationally triangulable connected one-dimensional unipotent affine algebraic subgroups of the Cremona groups are classified up to conjugacy.
 
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