Advanced Studies in Pure Mathematics

Bass' triangulability problem

Vladimir L. Popov

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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.

Article information

Algebraic Varieties and Automorphism Groups, K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg, eds. (Tokyo: Mathematical Society of Japan, 2017), 425-441

Received: 20 June 2015
Revised: 5 November 2015
First available in Project Euclid: 21 September 2018

Permanent link to this document euclid.aspm/1537498714

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E07: Birational automorphisms, Cremona group and generalizations

Cremona group unipotent group triangulability pure transcendental field extension


Popov, Vladimir L. Bass' triangulability problem. Algebraic Varieties and Automorphism Groups, 425--441, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510425.

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