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On some arithmetic problems related to the Hodge cycles on the Fermat varieties. (English) Zbl 0506.14030

Math. Ann. 266, 23-54 (1983); erratum ibid. 267, 572 (1984).

MSC:

14J25 Special surfaces
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14C22 Picard groups
11D41 Higher degree equations; Fermat’s equation
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References:

[1] Aoki, N., Shioda, T.: Generators of the Néron-Severi group of a Fermat surface (to appear) · Zbl 0586.14028
[2] Borevich, Z.I., Shafarevich, I.R.: Number theory. New York, London: Academic Press 1966 · Zbl 0145.04902
[3] Koblitz, N., Rohrlich, D.: Simple factors in the Jacobian of a Fermat curve. Can. J. Math.30, 1183-1205 (1978) · Zbl 0399.14023 · doi:10.4153/CJM-1978-099-6
[4] Koblitz, N., Ogus, A.: Algebraicity of some products of values of the ? function. Appendix to Deligne’s article in: AMS Proc. Symp. Pure Math.33, 343-345 (1979) · Zbl 0449.10029
[5] Kubert, D., Lang, S.: Modular units. Berlin, Heidelberg, New York: Springer 1981 · Zbl 0492.12002
[6] Kubert, D.: The universal ordinary distribution. Bull. Soc. Math. France107, 179-202 (1979) · Zbl 0409.12021
[7] Meyer, W., Neutsch, W.: Fermatquadrupel. Math. Ann.256, 51-62 (1981) · Zbl 0449.10014 · doi:10.1007/BF01450943
[8] Ran, Z.: Cycles on Fermat hypersurfaces. Compositio Math.42, 121-142 (1981) · Zbl 0463.14003
[9] Shioda, T.: the Hodge conjecture for Fermat varieties. Math. Ann.245, 175-184 (1979) · Zbl 0408.14012 · doi:10.1007/BF01428804
[10] Shioda, T.: On the Picard number of a Fermat surface. J. Fac. Sci. Univ. Tokyo.28, 725-734 (1982) · Zbl 0567.14021
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