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Borel, Armand

Some finiteness properties of adele groups over number fields. (English) Zbl 0135.08902

Publ. Math., Inst. Hautes Étud. Sci. 16, 101-126 (1963).
Reviewer: M. Kneser
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Cited in 2 Reviews
Cited in 81 Documents

MSC:

11R56 Adèle rings and groups
20G35 Linear algebraic groups over adèles and other rings and schemes

Keywords:

finiteness properties; adele groups over number fields

Citations:

Zbl 0107.14804; Zbl 0136.30101
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\textit{A. Borel}, Publ. Math., Inst. Hautes Étud. Sci. 16, 101--126 (1963; Zbl 0135.08902)
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References:

[1] A. Borel, Some properties of adele groups attached to algebraic groups,Bull. A.M.S., 67, (1961), p. 583–585. · Zbl 0119.37002
[2] —, Ensembles fondamentaux pour les groupes arithmétiques,Colloque sur la théorie des groupes algébriques, Bruxelles, 1962.
[3] —, Arithmetic properties of algebraic groups,Proc. Int. Congress of Math., Stockholm, 1962. · Zbl 0107.14804
[4] ——, Arithmetic subgroups of algebraic groups,Annals of Math. (2),75 (1962), p. 485–535. · Zbl 0107.14804
[5] — andJ.-P. Serre,Théorèmes de finitude en cohomologie galoisienne (en préparation).
[6] M. Eichler, Quadratische Formen und orthogonale Gruppen,Grund. Math. Wiss., LXIII, Springer, Berlin, 1952.
[7] R. Godement, Groupes linéaires algébriques sur un corps parfait,Sem. Bourbaki, no 206, Paris, 1960–61.
[8] M. Kneser, Approximation in algebraischen Gruppen,Colloque sur la théorie des groupes algébriques, Bruxelles, 1962.
[9] —, Einfach zusammenhängende algebraische Gruppen in der Arithmetik,Proc. Int. Congress Math., Stockholm, 1962.
[10] S. Lang andJ. Tate, Principal homogeneous spaces over abelian varieties,Amer. Jour. Math., 80 (1958), p. 659–684. · Zbl 0097.36203
[11] T. Ono, On some arithmetic properties of linear algebraic groups,Annals of Math. (2),70 (1959), p. 266–290. · Zbl 0092.26701
[12] M. Rosenlicht, Some rationality questions on algebraic groups,Annali di Mat. pura ed applic. (IV),63 (1957), p. 25–50. · Zbl 0079.25703
[13] J.-P. Serre,Corps locaux, Publ. Math. Inst. Nancago VIII, Hermann, Paris, 1962. · Zbl 0137.02601
[14] A. Weil,Adeles and algebraic groups (Notes byM. Demazure andT. Ono), The Institute for Advanced Study, Princeton, N.J., 1961.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.