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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 1, Pages 67–109 (Mi izv2291)  

This article is cited in 7 scientific papers (total in 8 papers)

Minimal models of curves of genus 2 and homomorphisms of abelian varieties defined over a field of finite characteristic

A. N. Parshin


Abstract: In this article, we prove a finiteness theorem for isogenous abelian varieties of dimension 2 defined over a field of algebraic functions of one variable whose characteristic $\ne2$. By means of this result, we prove Tate's conjecture on homomorphisms of abelian varieties of dimension 1 defined over the same field.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:1, 65–108

Bibliographic databases:

Document Type: Article
UDC: 513.61
MSC: Primary 14K05; Secondary 14E30, 14E35
Received: 01.07.1971

Citation: A. N. Parshin, “Minimal models of curves of genus 2 and homomorphisms of abelian varieties defined over a field of finite characteristic”, Izv. Akad. Nauk SSSR Ser. Mat., 36:1 (1972), 67–109; Math. USSR-Izv., 6:1 (1972), 65–108

Citation in format AMSBIB
\Bibitem{Par72}
\by A.~N.~Parshin
\paper Minimal models of curves of genus~2 and homomorphisms of abelian varieties defined over a~field of finite characteristic
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 1
\pages 67--109
\mathnet{http://mi.mathnet.ru/izv2291}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=316456}
\zmath{https://zbmath.org/?q=an:0246.14007}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 1
\pages 65--108
\crossref{https://doi.org/10.1070/IM1972v006n01ABEH001868}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. G. Zarhin, “A remark on endomorphisms of abelian varieties over function fields of finite characteristic”, Math. USSR-Izv., 8:3 (1974), 477–480  mathnet  crossref  mathscinet  zmath
    2. Yu. G. Zarhin, “Endomorphisms of abelian varieties over fields of finite characteristic”, Math. USSR-Izv., 9:2 (1975), 255–260  mathnet  crossref  mathscinet  zmath
    3. S. G. Tankeev, “O plyurikanonicheskikh otobrazheniyakh algebraicheskikh poverkhnostei osnovnogo tipa”, UMN, 30:6(186) (1975), 184–184  mathnet  mathscinet  zmath
    4. 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
    5. Nguyen Khac Viet, “On minimal models of algebraic curves”, Math. USSR-Sb., 67:1 (1990), 65–74  mathnet  crossref  mathscinet  zmath  isi
    6. J. R. Merriman, N. P. Smart, “Curves of genus 2 with good reduction away from 2 with a rational Weierstrass point”, Math Proc Camb Phil Soc, 114:2 (1993), 203  crossref  mathscinet  zmath
    7. Q. V. Pham, “An arithmetic Hurwitz formula”, Abh Math Semin Univ Hambg, 64:1 (1994), 51  crossref  mathscinet  zmath
    8. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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