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Manin homomorphisms for elliptic curves over a field of formal power series

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Abstract

In this paper we describe the intersection of the kernels of Manin homomorphisms for an arbitrary elliptic curve over a field of formal power series.

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Literature cited

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    Yu. I. Manin, “Algebraic curves over fields with differentiation,” Izv. Akad. Nauk SSSR, Ser. Matem.,22, 737–756 (1958).

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    Yu. I. Manin, “Rational points of algebraic curves over functional fields,” Izv. Akad. Nauk SSSR, Ser. Matem.,27, 1397–1442 (1963).

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    Yu. R. Vainberg, “Algebraic varieties over fields with differentiation,” Matem. Sb.,80 (122), No. 3 (11), 417–444 (1969).

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    E. Lutz, “Sur l'equation y2=x3−Ax−B dans le corps ℜ-adiques,” J. Reine u Angew. Math.,177, No. 4, 238–247 (1937).

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Additional information

Translated from Matematicheskie Zametki, Vol. 12, No. 4, pp. 425–432, October, 1972.

The author wishes to thank Yu. I. Manin for his attention to the paper.

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Vainberg, Y.R. Manin homomorphisms for elliptic curves over a field of formal power series. Mathematical Notes of the Academy of Sciences of the USSR 12, 688–692 (1972). https://doi.org/10.1007/BF01093675

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Keywords

  • Power Series
  • Elliptic Curve
  • Elliptic Curf
  • Formal Power Series
  • Arbitrary Elliptic Curve