Isogeny classes of abelian varieties over finite fields

Taira HONDA

doi:10.2969/jmsj/02010083

Taira HONDA

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1968 Volume 20 Issue 1-2 Pages 83-95

DOI https://doi.org/10.2969/jmsj/02010083

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Published: 1968 Received: July 24, 1967 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Shokichi Iyanaga on his 60th birthday

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941), 197-272.
2) H. Hasse, Zum Existenzsatz von Grunwald in Klassenkörpertheorie, J. Reine Angew. Math., 188 (1950), 40-64.
3) T. Honda, On the jacobian variety of the algebraic curve y²=1-x^l over a field of characteristic p>0, Osaka J. Math., 3 (1966), 189-194.
4) S. Lang, Abelian varieties, Interscience Tracts, New York, 1959.
5) Y. Manin, The theory of commutative formal groups over fields of finite characteristic, Russian Math. Surveys, 18 (1963), 1-81.
6) F. Oort, Commutative group schemes, Lecture Notes in Math., Springer, Berlin-Heidelberg-New York, 1966.
7) J.-P. Serre, L'Annuaire du College de France, 1964/65.
8) J.-P. Serre, Groupes p-divisible, Sem. Bourbaki, 318, 1966/67.
9) J.-P. Serre and J. Tate, Good reduction of abelian varieties and applications, to appear.
10) G. Shimura, On complex multiplications, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo-Nikko,1955, Science Council of Japan, 1956, 23-30.
11) G. Shimura, On the field of definition for a field of automorphic functions, I, II, III, Ann. of Math., 80 (1964), 160-189, 81 (1965), 124-165, 83 (1966), 377-385.
12) G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math., 85 (1967), 58-159.
13) G. Shimura and Y. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, No. 6, Tokyo, 1961.
14) Y. Taniyama, Jacobian varieties and number fields, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo-Nikko, 1955, Science Council of Japan, 1956, 31-45.
15) Y. Taniyama, L-functions of number fields and zeta functions of abelian varieties, J. Math. Soc. Japan, 9 (1957), 330-366.
16) J. Tate, Algebraic cycles and poles of zeta functions, Arithmetical algebraic geometry, 93-110, Harper and Row, New York, 1965.
17) J. Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math., 2 (1966), 134-144.
18) J. Tate, In preparation.
19) A. Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948.
20) A. Weil, On a certain type of characters of the idele-class group of an algebraic number-field, Proceedings of the International Symposium on Algebraic number Theory, Tokyo-Nikko, 1955, Science Council of Japan, 1956, 1-7.
21) A. Weil, The field of definition of a variety, Amer. J. Math., 78 (1956), 509-524.

Right : [1] M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941), 197-272.
[2] H. Hasse, Zum Existenzsatz von Grunwald in Klassenkörpertheorie, J. Reine Angew. Math., 188 (1950), 40-64.
[3] T. Honda, On the jacobian variety of the algebraic curve y²=1-x^l over a field of characteristic p>0, Osaka J. Math., 3 (1966), 189-194.
[4] S. Lang, Abelian varieties, Interscience Tracts, New York, 1959.
[5] Y. Manin, The theory of commutative formal groups over fields of finite characteristic, Russian Math. Surveys, 18 (1963), 1-81.
[6] F. Oort, Commutative group schemes, Lecture Notes in Math., Springer, Berlin-Heidelberg-New York, 1966.
[7] J. -P. Serre, L'Annuaire du College de France, 1964/65.
[8] J. -P. Serre, Groupes p-divisible, Sem. Bourbaki, 318, 1966/67.
[9] J. -P. Serre and J. Tate, Good reduction of abelian varieties and applications, to appear.
[10] G. Shimura, On complex multiplications, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo-Nikko,1955, Science Council of Japan, 1956, 23-30.
[11] G. Shimura, On the field of definition for a field of automorphic functions, I, II, III, Ann. of Math., 80 (1964), 160-189, 81 (1965), 124-165, 83 (1966), 377-385.
[12] G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math., 85 (1967), 58-159.
[13] G. Shimura and Y. Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, No. 6, Tokyo, 1961.
[14] Y. Taniyama, Jacobian varieties and number fields, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo-Nikko, 1955, Science Council of Japan, 1956, 31-45.
[15] Y. Taniyama, L-functions of number fields and zeta functions of abelian varieties, J. Math. Soc. Japan, 9 (1957), 330-366.
[16] J. Tate, Algebraic cycles and poles of zeta functions, Arithmetical algebraic geometry, 93-110, Harper and Row, New York, 1965.
[17] J. Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math., 2 (1966), 134-144.
[18] J. Tate, In preparation.
[19] A. Weil, Variétés abéliennes et courbes algébriques, Hermann, Paris, 1948.
[20] A. Weil, On a certain type of characters of the idèle-class group of an algebraic number-field, Proceedings of the International Symposium on Algebraic number Theory, Tokyo-Nikko, 1955, Science Council of Japan, 1956, 1-7.
[21] A. Weil, The field of definition of a variety, Amer. J. Math., 78 (1956), 509-524.

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