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Mat. Zametki, 1974, Volume 15, Issue 4, Pages 561–570 (Mi mz7379)  

Algebraic curves over functional fields with a finite field of constants

A. N. Parshin

Steklov Mathematical Institute, Academy of Sciences of the USSR

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.

Full text: PDF file (784 kB)

English version:
Mathematical Notes, 1974, 15:4, 330–335

Bibliographic databases:

Document Type: Article
UDC: 512
Received: 18.05.1972

Citation: A. N. Parshin, “Algebraic curves over functional fields with a finite field of constants”, Mat. Zametki, 15:4 (1974), 561–570; Math. Notes, 15:4 (1974), 330–335

Citation in format AMSBIB
\Bibitem{Par74}
\by A.~N.~Parshin
\paper Algebraic curves over functional fields with a~finite field of constants
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 4
\pages 561--570
\mathnet{http://mi.mathnet.ru/mz7379}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=476749}
\zmath{https://zbmath.org/?q=an:0299.14016|0295.14015}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 4
\pages 330--335
\crossref{https://doi.org/10.1007/BF01095123}


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