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September 14, 2016 10:30, International Cremona Conference, September 5--16, 2016, Basel, Switzerland  


Around the Bass' Triangulability Problem

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 concerning rational triangulability of unipotent algebraic subgroups of the affine Cremona groups.
The following topics will be discussed: a rational triangulability criterion; the existence of rationally non-triangulable connected solvable affine algebraic subgroups of the Cremona groups; stable rational triangulability of such subgroups (in particular, the affirmative answer to the Bass' Triangulability Problem in the stable range); a general theorem on invariant subfields of purely transcendental field extensions used for proving these results; a general construction of all rationally triangulable subgroups of the Cremona groups; application: the classification of all rationally triangulable connected one-dimensional unipotent affine algebraic subgroups of the Cremona groups up to conjugacy.

Language: English

Website: https://algebra.dmi.unibas.ch/blanc/cremonaconference
 
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