Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- 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
Bass' triangulability problem
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.
Received: 20 June 2015
Revised: 5 November 2015
First available in Project Euclid: 21 September 2018
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14E07: Birational automorphisms, Cremona group and generalizations
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. https://projecteuclid.org/euclid.aspm/1537498714