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This article is cited in 8 scientific papers (total in 9 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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Mathematics of the USSR-Izvestiya, 1972, 6:1, 65–108
Bibliographic databases:
 
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
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\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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http://mi.mathnet.ru/eng/izv2291 http://mi.mathnet.ru/eng/izv/v36/i1/p67
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This publication is cited in the following articles:
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Yu. G. Zarhin, “A remark on endomorphisms of abelian varieties over function fields of finite characteristic”, Math. USSR-Izv., 8:3 (1974), 477–480
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Yu. G. Zarhin, “Endomorphisms of abelian varieties over fields of finite characteristic”, Math. USSR-Izv., 9:2 (1975), 255–260
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S. G. Tankeev, “O plyurikanonicheskikh otobrazheniyakh algebraicheskikh poverkhnostei osnovnogo tipa”, UMN, 30:6(186) (1975), 184–184
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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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Nguyen Khac Viet, “On minimal models of algebraic curves”, Math. USSR-Sb., 67:1 (1990), 65–74
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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
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Q. V. Pham, “An arithmetic Hurwitz formula”, Abh Math Semin Univ Hambg, 64:1 (1994), 51
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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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S. G. Tankeev, “On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci”, Izv. Math., 83:3 (2019), 613–653
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