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Finiteness theorem for isogenies of abelian varieties over function fields of finite characteristic. (English. Russian original) Zbl 0324.14009

Funct. Anal. Appl. 8, 301-303 (1974); translation from Funkts. Anal. Prilozh. 8, No. 4, 31-34 (1974).

MSC:

14K10 Algebraic moduli of abelian varieties, classification
14K05 Algebraic theory of abelian varieties
14H05 Algebraic functions and function fields in algebraic geometry
14K15 Arithmetic ground fields for abelian varieties
14J10 Families, moduli, classification: algebraic theory
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References:

[1] Yu. G. Zarkhin and Yu. I. Manin, ”Height on families of Abelian varieties,” Matem. Sb.,89, No. 2, 171-181 (1972). · Zbl 0256.14018
[2] D. Mumford, Abelian Varieties, Oxford University Press, London (1970).
[3] D. Mumford, ”On the equations defining Abelian varieties, I, II,” Inv. Math.,1, No. 4, 287-354 (1966);3, No. 2, 75-135 (1967). · Zbl 0219.14024 · doi:10.1007/BF01389737
[4] A. N. Parshin, ”Minimal models of curves of genus 2 and homomorphisms of Abelian varieties defined over fields of finite characteristic,” Izv. Akad. Nauk SSSR, Ser. Matem.,36, 67-109 (1972). · Zbl 0246.14007
[5] A. N. Parshin, ”Quelques conjectures de finitude en Geometrie Diophantienee,” Actes Congres Intern. Math, Nice (1970).
[6] A. N. Parshin, ”Isogenies and torsion of elliptic curves,” Izv. Akad. Nauk SSSR, Ser. Matem.,34, 409-424 (1970).
[7] J.-P. Serre, Abelianl-adic Representations and Elliptic Curves, Benjamin (1968).
[8] J.-P. Serre and J. Tate, ”Good reduction of Abelian varieties,” Ann. Math.,88, 492-517 (1968). · Zbl 0172.46101 · doi:10.2307/1970722
[9] J. Tate, ”Endomorphisms of Abelian varieties over finite fields,” Inv. Math.,2, 134-144 (1966). · Zbl 0147.20303 · doi:10.1007/BF01404549
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