Cohomology of fiber systems and Mordell-Weil groups of abelian varieties
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Duke Mathematical Journal

Cohomology of fiber systems and Mordell-Weil groups of abelian varieties

Alice Silverberg

Source: Duke Math. J. Volume 56, Number 1 (1988), 41-46.

First Page PDF: View first page of article (PDF, 109 KB)

Primary Subjects: 11G18
Secondary Subjects: 11F75, 14D20, 14K10, 22E40, 22E46, 32L10

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077306452
Mathematical Reviews number (MathSciNet): MR932856
Zentralblatt MATH identifier: 0645.14019
Digital Object Identifier: doi:10.1215/S0012-7094-88-05603-7

References

[1], Algebraic Groups and Discrete Subgroups, Proc. Sympos. Pure Math., vol. 9, Providence, Amer. Math. Soc., 1966.
[2] A. Borel, Density and maximality of arithmetic subgroups, J. Reine Angew. Math. 224 (1966), 78–89.
Mathematical Reviews (MathSciNet): MR34:5824
Zentralblatt MATH: 0158.03105
[3] A. Borel, Stable real cohomology of arithmetic groups. II, Manifolds and Lie groups (Notre Dame, Ind., 1980), Progr. Math., vol. 14, Birkhäuser Boston, Mass., 1981, pp. 21–55.
Mathematical Reviews (MathSciNet): MR83h:22023
Zentralblatt MATH: 0483.57026
[4] A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, vol. 94, Princeton University Press, Princeton, N.J., 1980.
Mathematical Reviews (MathSciNet): MR83c:22018
Zentralblatt MATH: 0443.22010
[5] S. Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York, 1962.
Mathematical Reviews (MathSciNet): MR26:2986
Zentralblatt MATH: 0111.18101
[6] Michio Kuga, Fiber varieties over a symmetric space whose fibers are abelian varieties, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 338–346.
Mathematical Reviews (MathSciNet): MR34:5990
Zentralblatt MATH: 0173.48902
[7] S. Lang, Diophantine geometry, Interscience Tracts in Pure and Applied Mathematics, No. 11, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962.
Mathematical Reviews (MathSciNet): MR26:119
Zentralblatt MATH: 0115.38701
[8]1 Y. Matsushima and S. Murakami, On certain cohomology groups attached to Hermitian symmetric spaces, Osaka J. Math. 2 (1965), 1–35.
Mathematical Reviews (MathSciNet): MR32:1728
Zentralblatt MATH: 0142.19503
Project Euclid: euclid.ojm/1200685925
[8]2 Y. Matsushima and S. Murakami, On certain cohomology groups attached to Hermitian symmetric spaces. II, Osaka J. Math. 5 (1968), 223–241.
Mathematical Reviews (MathSciNet): MR42:1145
Zentralblatt MATH: 0183.26103
Project Euclid: euclid.ojm/1200692169
[9] Y. Matsushima and G. Shimura, On the cohomology groups attached to certain vector valued differential forms on the product of the upper half planes, Ann. of Math. (2) 78 (1963), 417–449.
Mathematical Reviews (MathSciNet): MR27:5274
Zentralblatt MATH: 0141.38704
Digital Object Identifier: doi:10.2307/1970534
JSTOR: links.jstor.org
[10] M. S. Raghunathan, On the first cohomology of discrete subgroups of semisimple Lie groups, Amer. J. Math. 87 (1965), 103–139.
Mathematical Reviews (MathSciNet): MR30:3940
Zentralblatt MATH: 0132.02102
Digital Object Identifier: doi:10.2307/2373227
JSTOR: links.jstor.org
[11]1 M. S. Raghunathan, Cohomology of arithmetic subgroups of algebraic groups. I, Ann. of Math. (2) 86 (1967), 409–424.
Mathematical Reviews (MathSciNet): MR37:2898
Zentralblatt MATH: 0157.06802
Digital Object Identifier: doi:10.2307/1970585
[11]2 M. S. Raghunathan, Cohomology of arithmetic subgroups of algebraic groups. II, Ann. of Math. (2) 87 (1967), 279–304.
Mathematical Reviews (MathSciNet): MR37:2898
Zentralblatt MATH: 0157.06803
Digital Object Identifier: doi:10.2307/1970585
[12] M. S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, New York, 1972.
Mathematical Reviews (MathSciNet): MR58:22394a
Zentralblatt MATH: 0254.22005
[13] I. Satake, Algebraic structures of symmetric domains, Kanô Memorial Lectures, vol. 4, Iwanami Shoten, Tokyo, 1980.
Mathematical Reviews (MathSciNet): MR82i:32003
Zentralblatt MATH: 0483.32017
[14] G. Shimura, Moduli and fibre systems of abelian varieties, Ann. of Math. (2) 83 (1966), 294–338.
Mathematical Reviews (MathSciNet): MR33:7339
Zentralblatt MATH: 0141.37503
Digital Object Identifier: doi:10.2307/1970434
JSTOR: links.jstor.org
[15] G. Shimura, Discontinuous groups and abelian varieties, Math. Ann. 168 (1967), 171–199.
Mathematical Reviews (MathSciNet): MR37:6289
Zentralblatt MATH: 0145.17401
Digital Object Identifier: doi:10.1007/BF01361553
[16] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan 24 (1972), 20–59.
Mathematical Reviews (MathSciNet): MR55:2927
Zentralblatt MATH: 0226.14013
[17] A. Silverberg, Mordell-Weil groups of generic abelian varieties, Invent. Math. 81 (1985), no. 1, 71–106.
Mathematical Reviews (MathSciNet): MR87b:11046
Zentralblatt MATH: 0576.14020
Digital Object Identifier: doi:10.1007/BF01388773
[18] A. Silverberg, Mordell-Weil groups of generic abelian varieties in the unitary case, preprint.
Mathematical Reviews (MathSciNet): MR929425
Digital Object Identifier: doi:10.2307/2046781

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