Abelian surfaces and jacobian varieties over finite fields

Hans-Georg Rück

Compositio Mathematica (1990)

  • Volume: 76, Issue: 3, page 351-366
  • ISSN: 0010-437X

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Rück, Hans-Georg. "Abelian surfaces and jacobian varieties over finite fields." Compositio Mathematica 76.3 (1990): 351-366. <http://eudml.org/doc/90061>.

@article{Rück1990,
author = {Rück, Hans-Georg},
journal = {Compositio Mathematica},
keywords = {Weil numbers; smooth curve over a field; zeta function; Riemann hypothesis; abelian varieties over finite fields},
language = {eng},
number = {3},
pages = {351-366},
publisher = {Kluwer Academic Publishers},
title = {Abelian surfaces and jacobian varieties over finite fields},
url = {http://eudml.org/doc/90061},
volume = {76},
year = {1990},
}

TY - JOUR
AU - Rück, Hans-Georg
TI - Abelian surfaces and jacobian varieties over finite fields
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 76
IS - 3
SP - 351
EP - 366
LA - eng
KW - Weil numbers; smooth curve over a field; zeta function; Riemann hypothesis; abelian varieties over finite fields
UR - http://eudml.org/doc/90061
ER -

References

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  1. [H-N] Hayashida, T.- Nishi, M.: Existence of curves of genus two on a product of two elliptic curves, J. Math. Soc. Japan, Vol. 17 (1965), 1-16. Zbl0132.41701MR201434
  2. [L] Lang, S.: Algebraic groups over finite fields, Amer. J. of Math.78 (1956), 555-563. Zbl0073.37901MR86367
  3. [Ma] Manin, Y.I.: The Theory of commutative formal groups over fields of finite characteristic, Russian Math. Surv., Vol. 18 (1963), 1-83. Zbl0128.15603MR157972
  4. [M] Mumford, D.: Abelian Varieties, Second Edition, Oxford Univ. Press, Oxford (1974). Zbl0326.14012
  5. [O] Oda T.: The first de Rham cohomology group and Dieudonné modules, Ann. scient. Éc. Norm. Sup., (4), t. 2 (1969), 63-135. Zbl0175.47901MR241435
  6. [R] Ramanujam, C.P.: The Theorem of Tate, Appendix I in [M]. 
  7. [T] Tate, J.: Endomorphisms of abelian varieties over finite fields, Invent. Math., Vol. 2 (1966), 134-144. Zbl0147.20303MR206004
  8. [T-H] Tate, J.: Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda), Sem. Bourbaki358, 1968-1969. Zbl0212.25702
  9. [Wa] Waterhouse, W.C.: Abelian varieties over finite fields, Ann. scient. Éc. Norm. Sup., (4), t. 2 (1969), 521-560. Zbl0188.53001MR265369
  10. [W] Weil, A.: Zum Beweis des Torellischen Satzes, Nachr. Akad. Wiss Göttingen, Math.-Phys. Kl. (1957), 33-53. Zbl0079.37002MR89483
  11. [We] Weiss, E.: Algebraic Number Theory, McGraw-Hill, New-York (1963). Zbl0115.03601MR159805

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