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Serre Lie algebras of generalized Jacobians

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Abstract

In this work we construct an example of a generalized Jacobian of an elliptic curve defined over a field of algebraic numbers k such that the Serre Lie algebra p-adic representation of the Galois group of the algebraic closure of the field k in its Tate module is irreducible.

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Literature cited

  1. J. P. Serre, “Sur les groupes de congruence des variétés abéliennes,” Izv. Akad. Nauk SSSR,28, No. 1, 2–30 (1964).

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  3. J. P. Serre, Abelianl-Additive Representations and Elliptic Curves [Russian translation], Mir, Moscow (1973).

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  4. J. Tate, “Algebraic classes of cohomology,” Usp. Matem. Nauk,20, No. 6, 27–40 (1965).

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  5. A. Robert, Elliptic Curves, Lecture Notes in Math., Vol. 326, Springer-Verlag, Berlin-New York (1969).

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Authors and Affiliations

  1. L'vov Branch of the Mathematical Physics Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, USSR

    G. V. Belyi & V. A. Korolevich

Authors
  1. G. V. Belyi
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  2. V. A. Korolevich
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Additional information

Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 571–576, April, 1976.

In conclusion the authors thank O. N. Vvedenskii for guidance in this work.

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Belyi, G.V., Korolevich, V.A. Serre Lie algebras of generalized Jacobians. Mathematical Notes of the Academy of Sciences of the USSR 19, 347–349 (1976). https://doi.org/10.1007/BF01156795

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  • DOI: https://doi.org/10.1007/BF01156795

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