T. Kambayashi, M. Miyanishi, M. Takeuchi, "Unipotent Algebraic Groups"
1974 | pages: 170 | ISBN: 3540069607, 0387069607| PDF | 4,1 mb
The geometry and group theory of unipotent algebraic groups over an arbitrary ground field were successfully pioneered by Rosenlicht in the late fifties and early sixties. In the subsequent years not very much was added to the knowledge in this area, with only a few notable contributions such as those by Russell and by Tits. Lately, however, there have been indications of growing interest in this and related subject areas (affine space , its automorphisms , purely inseparable cohomology theories , ... ). Even as the present paper was undergoing the final redaction, a graduate student in Tokyo settled our conjecture in Section 5 by constructing an elaborate counter-example; one of the coauthors established the absence of nontrivial separable forms of the affine plane, confirming an earlier announcement of Shafarevich; another found a description of the category of all commutative affine group schemes over an imperfect field by extending Schoeller's work; and still another obtained an algebraic characterization of the affine plane.