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This article is cited in 16 scientific papers (total in 17 papers)
Algebraic curves over function fields. I
A. N. Parshin
Abstract:
This paper studies the diophantine geometry of curves of genus greater than unity defined over a one-dimensional function field.
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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:5, 1145–1170
Bibliographic databases:
 
UDC:
513.6
MSC: 11G30, 11G35, 11G05, 11F46, 14H20
Received: 07.05.1968
Citation:
A. N. Parshin, “Algebraic curves over function fields. I”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1191–1219; Math. USSR-Izv., 2:5 (1968), 1145–1170
Citation in format AMSBIB
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\by A.~N.~Parshin
\paper Algebraic curves over function fields. I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 5
\pages 1191--1219
\mathnet{http://mi.mathnet.ru/izv2513}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=257086}
\zmath{https://zbmath.org/?q=an:0181.23902|0188.53003}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1145--1170
\crossref{https://doi.org/10.1070/IM1968v002n05ABEH000723}
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http://mi.mathnet.ru/eng/izv2513 http://mi.mathnet.ru/eng/izv/v32/i5/p1191
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This publication is cited in the following articles:
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S. Yu. Arakelov, “Families of algebraic curves with fixed degeneracies”, Math. USSR-Izv., 5:6 (1971), 1277–1302
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A. N. Parshin, “Minimal models of curves of genus 2 and homomorphisms of abelian varieties defined over a field of finite characteristic”, Math. USSR-Izv., 6:1 (1972), 65–108
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Frans Oort, “Subvarieties of moduli spaces”, Invent math, 24:2 (1974), 95
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A. N. Rudakov, I. R. Shafarevich, “Inseparable morphisms of algebraic surfaces”, Math. USSR-Izv., 10:6 (1976), 1205–1237
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Spencer Bloch, “The proof of the mordell conjecture”, Math Intelligencer, 6:2 (1984), 41
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R. C. Mason, “Norm form equations IV: Rational functions”, Mathematika, 33:2 (1986), 204
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M. G. Zaidenberg, “Isotrivial families of curves on affine surfaces and characterization of the affine plane”, Math. USSR-Izv., 30:3 (1988), 503–532
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Junjiro Noguchi, “Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces”, Invent Math, 93:1 (1988), 15
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M. G. Zaidenberg, “A function-field analog of the Mordell conjecture: a noncompact version”, Math. USSR-Izv., 35:1 (1990), 61–81
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A. N. Parshin, “On the application of ramified coverings in the theory of Diophantine equations”, Math. USSR-Sb., 66:1 (1990), 249–264
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Sheng-Li Tan, “On the invariants of base changes of pencils of curves, I”, manuscripta math, 84:1 (1994), 225
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Sheng-Li Tan, “On the invariants of base changes of pencils of curves, II”, Math Z, 222:1 (1996), 655
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Khac Viet Nguyen, “On families of curves over 1 with small number of singular fibres”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:4 (1998), 459
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Hui Lan, “A Note on Height Inequality”, Comm. in Algebra, 34:4 (2006), 1205
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S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197
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Marc Hindry, Amílcar Pacheco, “An analogue of the Brauer–Siegel theorem for abelian varieties in positive characteristic”, Mosc. Math. J., 16:1 (2016), 45–93
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S. O. Gorchinskiy, Vik. S. Kulikov, A. N. Parshin, V. L. Popov, “Igor Rostislavovich Shafarevich and His Mathematical Heritage”, Proc. Steklov Inst. Math., 307 (2019), 1–21
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