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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On a case of extensions of group schemes


Author: B. Weisfeiler
Journal: Trans. Amer. Math. Soc. 248 (1979), 171-189
MSC: Primary 14L15; Secondary 20G10
MathSciNet review: 521699
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Abstract: The extensions of a smooth connected commutative group scheme whose generic fiber is $ {G_m}$ by the additive group scheme are studied. The results are most explicit in the case when the basic scheme is the spectrum of an integral domain containing a field.


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  • [1] Séminaire de Géométrie Algébrique 1962/1964 dirigé par M. Demazure et A. Grothendieck, Schémas en groupes. II, Lecture Notes in Math., vol. 152, Springer-Verlag, Berlin, 1970.
  • [2] Michel Demazure and Pierre Gabriel, Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970 (French). Avec un appendice Corps de classes local\ par Michiel Hazewinkel. MR 0302656 (46 #1800)
  • [3] Michel Raynaud, Faisceaux amples sur les schémas en groupes et les espaces homogènes, Lecture Notes in Mathematics, Vol. 119, Springer-Verlag, Berlin-New York, 1970 (French). MR 0260758 (41 #5381)
  • [4] B. Ju. Veĭsfeĭler and I. V. Dolgačev, Unipotent group schemes over integral rings, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 757–799 (Russian). MR 0376697 (51 #12872)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0521699-9
PII: S 0002-9947(1979)0521699-9
Article copyright: © Copyright 1979 American Mathematical Society