On a theorem of Tate

• Autorzy: Fedor Bogomolov , Yuri Tschinkel
• Języki publikacji: EN

Abstrakty

EN

We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.

Słowa kluczowe

EN

finite fields; abelian varieties; Tate classes

Kategorie tematyczne

• 14K02: Isogeny
• 14G15: Finite ground fields

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 3
• Strony: 343-350

Daty

wydano

2008-09-01

online

2008-07-02

Twórcy

autor

Fedor Bogomolov

• Courant Institute, NYU

autor

Yuri Tschinkel

Bibliografia

• [1] Bogomolov F., Korotiaev M., Tschinkel Y., A Torelli theorem for curves over finite fields, preprint available at http://arxiv.org/abs/0802.3708
• [2] Corvaja P., Zannier U., Finiteness of integral values for the ratio of two linear recurrences, Invent. Math., 2002, 149, 431–451 http://dx.doi.org/10.1007/s002220200221
• [3] Deligne P., La conjecture de Weil I, Inst. Hautes Études Sci. Publ. Math., 1974, 43, 273–307 http://dx.doi.org/10.1007/BF02684373
• [4] Honda T., Isogeny classes of abelian varieties over finite fields, J. Math. Soc. Japan, 1968, 20, 83–95 http://dx.doi.org/10.2969/jmsj/02010083
• [5] Magagna C., A lower bound for the r-order of a matrix modulo N, Monatsh. Math., 2008, 153, 59–81 http://dx.doi.org/10.1007/s00605-007-0484-2
• [6] Tate J., Endomorphisms of abelian varieties over finite fields, Invent. Math., 1966, 2, 134–144 http://dx.doi.org/10.1007/BF01404549
• [7] Tate J., Classes d’isogénie des variétés abéliennes sur un corps fini, In: Séminaire Bourbaki, Vol. 1968/69, Exposés 347–363, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1971, 179, 95–110 http://dx.doi.org/10.1007/BFb0058807
• [8] Zarhin Y.G., Abelian varieties, l-adic representations and Lie algebras. Rank independence on l, Invent. Math., 1979, 55, 165–176 http://dx.doi.org/10.1007/BF01390088

Identyfikatory

DOI

10.2478/s11533-008-0037-5