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VOL. 75 | 2017 Bass' triangulability problem
Vladimir L. Popov

Editor(s) Kayo Masuda, Takashi Kishimoto, Hideo Kojima, Masayoshi Miyanishi, Mikhail Zaidenberg


Exploring Bass' Triangulability Problem on unipotent algebraic subgroups of the affine Cremona groups, we prove a triangulability criterion, the existence of nontriangulable connected solvable affine algebraic subgroups of the Cremona groups, and stable triangulability of such subgroups; in particular, in the stable range we answer Bass' Triangulability Problem in the affirmative. To this end we prove a theorem on invariant subfields of 1-extensions. We also obtain a general construction of all rationally triangulable subgroups of the Cremona groups and, as an application, classify rationally triangulable connected one-dimensional unipotent affine algebraic subgroups of the Cremona groups up to conjugacy.


Published: 1 January 2017
First available in Project Euclid: 21 September 2018

zbMATH: 1396.14015
MathSciNet: MR3793371

Digital Object Identifier: 10.2969/aspm/07510425

Primary: 14E07

Rights: Copyright © 2017 Mathematical Society of Japan


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