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Regular version of the site

Article

Подгруппы групп Кремоны: проблема Басса

A general theorem on the purity of of invariant field extensions
is proved. Using it, a criterion of rational triangulability of connected solvable
affine algebraic subgroups of the Cremona groups is obtained. This criterion is
applied for proving the existence of rationally nontriangulable subgroups of the
above form and for proving their stable rational triangulability. The latter property
answers in the affirmative Bass’ Triangulability Problem in the stable range. A
general construction of all rationally triangulable connected solvable affine algebraic
subgroups of the Cremona groups is obtained. As an application, a classification
of all rationally triangulable connected one-dimensional unipotent affine algebraic
subgroups of the Cremona groups up to conjugacy is given.