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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 5, Pages 1191–1219 (Mi izv2513)  

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
\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
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1145--1170

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    This publication is cited in the following articles:
    1. S. Yu. Arakelov, “Families of algebraic curves with fixed degeneracies”, Math. USSR-Izv., 5:6 (1971), 1277–1302  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  mathscinet  zmath
    3. Frans Oort, “Subvarieties of moduli spaces”, Invent math, 24:2 (1974), 95  crossref  mathscinet  zmath
    4. A. N. Rudakov, I. R. Shafarevich, “Inseparable morphisms of algebraic surfaces”, Math. USSR-Izv., 10:6 (1976), 1205–1237  mathnet  crossref  mathscinet  zmath
    5. Spencer Bloch, “The proof of the mordell conjecture”, Math Intelligencer, 6:2 (1984), 41  crossref  mathscinet  zmath
    6. R. C. Mason, “Norm form equations IV: Rational functions”, Mathematika, 33:2 (1986), 204  crossref  isi
    7. M. G. Zaidenberg, “Isotrivial families of curves on affine surfaces and characterization of the affine plane”, Math. USSR-Izv., 30:3 (1988), 503–532  mathnet  crossref  mathscinet  zmath
    8. Junjiro Noguchi, “Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces”, Invent Math, 93:1 (1988), 15  crossref
    9. M. G. Zaidenberg, “A function-field analog of the Mordell conjecture: a noncompact version”, Math. USSR-Izv., 35:1 (1990), 61–81  mathnet  crossref  mathscinet  zmath
    10. A. N. Parshin, “On the application of ramified coverings in the theory of Diophantine equations”, Math. USSR-Sb., 66:1 (1990), 249–264  mathnet  crossref  mathscinet  zmath  isi
    11. Sheng-Li Tan, “On the invariants of base changes of pencils of curves, I”, manuscripta math, 84:1 (1994), 225  crossref  mathscinet  zmath
    12. Sheng-Li Tan, “On the invariants of base changes of pencils of curves, II”, Math Z, 222:1 (1996), 655  crossref  mathscinet  zmath  isi
    13. 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  crossref
    14. Hui Lan, “A Note on Height Inequality”, Comm. in Algebra, 34:4 (2006), 1205  crossref
    15. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. 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  mathnet  crossref  mathscinet
    17. 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  mathnet  crossref  crossref  mathscinet  isi  elib
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