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Algebraic curves over functional fields with a finite field of constants

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Abstract

We prove a theorem of finiteness for curves of genus g>1, defined over a functional field of finite characteristic and having fixed invariants. As an application we obtain Tate's conjecture concerning homomorphisms of elliptic curves over a field of functions.

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR

    A. N. Parshin

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  1. A. N. Parshin
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Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 561–570, April, 1974.

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Parshin, A.N. Algebraic curves over functional fields with a finite field of constants. Mathematical Notes of the Academy of Sciences of the USSR 15, 330–335 (1974). https://doi.org/10.1007/BF01095123

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  • DOI: https://doi.org/10.1007/BF01095123

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