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On some Dualities Concerning Abelian Varieties

Published online by Cambridge University Press:  22 January 2016

Hideyuki Matsumura  and
Masayoshi Miyanishi
Hideyuki Matsumura
Affiliation:
Department of Mathematics, Kyoto University
Masayoshi Miyanishi
Affiliation:
Department of Mathematics, Kyoto University
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The group of extensions Ext(A, Ga) and Ext(A, Gm) of an abelian variety A by the additive or multiplicative group Ga, Gm have been investigated in detail ([9], [10], [GACC]). On the other hand, F. Oort [8] and M. Miyanishi [6] recently studied the groups Ext(Ga, A) and Ext(Gm, A). The purpose of the present paper is to clarify the relationship between these groups. Our results show that the latter groups can be derived from the former.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 447 - 462
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Barsotti, I.: Analytical methods for abelian varieties in positive characteristic, Colloque sur la théorie des groupes algébrique, Bruxelles 1962.Google Scholar
[2] Cartier, P.: Groupes algébriques et groupes formels, Colloque sur la théorie des groupes algébrique, Bruxelles 1962.Google Scholar
[3] Gabriel, P.: Sur les catégories localement noetheriennes et leurs applications aux algebres étudiées par Dieudonné (Groupes formels), Séminaire J. P. Serre (1960).Google Scholar
[4] Grothendieck, A.: Technique de descente III, Séminaire Bourbaki, t. 13, 1960/61, no. 212.Google Scholar
[5] Lang, S.: Abelian Varieties, Interscience, New York 1959.Google Scholar
[6] Miyanishi, M.: On the extensions of linear groups by abelian varieties over a field of positive characteristic p , to appear on the J. of Math. Soc. Japan.Google Scholar
[7] Mumford, D.: Lectures on Curves on an Algebraic Surface, mimeographed, Harvard University 1964.Google Scholar
[8] Oort, F.: To appear.Google Scholar
[9] Rosenlicht, M.: Extensions of vector groups by Abelian varieties, Amer. J. of Math. Vol. 80 (1958), 685–714.Google Scholar
[10] Serre, J. P.: Quelques propriétés des variétés abéliennes en caractéristique p , Amer. J. of Math. Vol. 80 (1958), 715–739.CrossRefGoogle Scholar
[11] Serre, J. P.: Groupes Algébriques et Corps de Classes, Hermann, Paris, 1959. cited as [GACC].Google Scholar
[12] Weil, A.: Variétés Abéliennes et Courbes Algébriques, Hermann, Paris 1948.Google Scholar
[13] Barsotti, I.: Abelian varieties over fields of positive characteristic, Rend. Circ. Mat. Palermo, 5, 1956, 1–25.Google Scholar