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Hazama, Fumio

Algebraic cycles on Abelian varieties with many real endomorphisms. (English) Zbl 0497.14017

Tohoku Math. J., II. Ser. 35, 303-308 (1983).
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Cited in 3 Documents

MSC:

14K15 Arithmetic ground fields for abelian varieties
14Pxx Real algebraic and real-analytic geometry
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14C99 Cycles and subschemes
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)

Keywords:

endomorphism ring of abelian variety; totally real fields; Hodge conjecture; Hodge ring; jacobian of modular curve
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References:

[1] N. BOURBAKI, Groupes et algebres de Lie, Hermann, Paris, 1960.
[2] J. GIRAUD, Modules des varietes abeliennes et varietes de Shimura, Varietes de Shimur et founctions L, Publications Mathematiques de L’Universite de Paris, VII, 6, 1981, 21-42. · Zbl 0538.14030
[3] H. IMAI, On the Hodge groups of some abelian varieties, Kodai Math. Sem. Rep. 2 (1976), 367-372. · Zbl 0328.14015 · doi:10.2996/kmj/1138847263
[4] D. MUMFORD, A note on Shimura’s paper ”Discontinuous groups and abelian varieties, Math. Ann. 181 (1969), 345-351. · Zbl 0169.23301 · doi:10.1007/BF01350672
[5] D. MUMFORD, Abelian varieties, Tata Inst. and Oxford Univ. Press, 1970 · Zbl 0223.14022
[6] T. MURASAKI, On rational cohomology classes of type (p, p) on an abelian variety, Sci Rep. Tokyo Kyoiku Daigaku, Sect. A, 10 (1969), 66-74. · Zbl 0176.18301
[7] V. P. MURTY, Algebraic cycles on abelian varieties, Ph. D. thesis, Harvard Univ., 1982 · Zbl 0482.06002
[8] K. A. RIBET, Galois action on division points of abelian varieties with many rea multiplications, Amer. J. Math. 98 (1976), 751-804. JSTOR: · Zbl 0348.14022 · doi:10.2307/2373815
[9] G. SHIMURA, On elliptic curves with complex multiplication as factors of the Jacobian of modular function fields, Nagoya Math. J. 43 (1971), 199-208. · Zbl 0225.14015
[10] S. G. TANKEEV, On algebraic cycles on abelian varieties, II. Izv. Akad. Nauk SSSR. 4 (1979), 418-429. · Zbl 0409.14008
[11] J. TATE, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry, Harper and Row, New York, 1965, 93-110. · Zbl 0213.22804
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