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Regular version of the site

Book chapter

Bass' triangulability problem

P. 425-441.

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.











In book

Vol. 75: Algebraic Varieties and Automorphism Groups. The Mathematical Society of Japan, 2017.