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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 4, Pages 731–752 (Mi izv1271)  

A function-field analog of the Mordell conjecture: a noncompact version

M. G. Zaidenberg


Abstract: The author proves a geometric analog of Manin's theorem on curves over function fields in the noncompact complex analytic situation. The proof relies on a “theorem on domination” in which the construction of the semistable reduction of a family of noncompact curves is carried out in terms of hyperbolic complex analysis.
Bibliography: 23 titles.

Full text: PDF file (2748 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:1, 61–81

Bibliographic databases:

UDC: 512.725 + 512.774.3+515.171.7 + 515.176.4
MSC: 11G30, 14H15, 32J25
Received: 21.10.1987

Citation: M. G. Zaidenberg, “A function-field analog of the Mordell conjecture: a noncompact version”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 731–752; Math. USSR-Izv., 35:1 (1990), 61–81

Citation in format AMSBIB
\Bibitem{Zai89}
\by M.~G.~Zaidenberg
\paper A~function-field analog of the Mordell conjecture: a~noncompact version
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 4
\pages 731--752
\mathnet{http://mi.mathnet.ru/izv1271}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1018745}
\zmath{https://zbmath.org/?q=an:0704.14020}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 1
\pages 61--81
\crossref{https://doi.org/10.1070/IM1990v035n01ABEH000686}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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