On a theorem of Tate
Fedor Bogomolov; Yuri Tschinkel
Open Mathematics (2008)
- Volume: 6, Issue: 3, page 343-350
- ISSN: 2391-5455
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topFedor Bogomolov, and Yuri Tschinkel. "On a theorem of Tate." Open Mathematics 6.3 (2008): 343-350. <http://eudml.org/doc/269397>.
@article{FedorBogomolov2008,
abstract = {We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.},
author = {Fedor Bogomolov, Yuri Tschinkel},
journal = {Open Mathematics},
keywords = {finite fields; abelian varieties; Tate classes; finite field},
language = {eng},
number = {3},
pages = {343-350},
title = {On a theorem of Tate},
url = {http://eudml.org/doc/269397},
volume = {6},
year = {2008},
}
TY - JOUR
AU - Fedor Bogomolov
AU - Yuri Tschinkel
TI - On a theorem of Tate
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 343
EP - 350
AB - We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.
LA - eng
KW - finite fields; abelian varieties; Tate classes; finite field
UR - http://eudml.org/doc/269397
ER -
References
top- [1] Bogomolov F., Korotiaev M., Tschinkel Y., A Torelli theorem for curves over finite fields, preprint available at http://arxiv.org/abs/0802.3708 Zbl1193.14036
- [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 Zbl1026.11021
- [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 Zbl0203.53302
- [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 Zbl1156.11013
- [6] Tate J., Endomorphisms of abelian varieties over finite fields, Invent. Math., 1966, 2, 134–144 http://dx.doi.org/10.1007/BF01404549 Zbl0147.20303
- [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 Zbl0406.14026
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