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Some results on the Mordell-Weil group of the Jacobian of the Fermat curve. (English) Zbl 0369.14011

MSC:
14G25 Global ground fields in algebraic geometry
14G05 Rational points
14H25 Arithmetic ground fields for curves
14H40 Jacobians, Prym varieties
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[1] Bashmakov, M.I.: The Cohomology of Abelian Varieties over a Number Field. Russ. Math. Surveys27, 25-70 (1972) · Zbl 0256.14016 · doi:10.1070/RM1972v027n06ABEH001392
[2] Birman, A.: Proof and Examples that the Equation of Fermat’s Last Theorem is Solvable in Integral Quaternions. Riveon Lematematika4, pp. 62-64. In Hebrew, with English summary (1950)
[3] Borevich, Z., Shafarevich, I.: Number Theory. New York: Academic Press 1966 · Zbl 0145.04902
[4] Carlitz, L., Olson, F.R.: Maillet’s Determinat. Proc. Amer. Math. Soc.6, 265-269 (1955) · Zbl 0065.02703
[5] Deligne, P.: Variétés Abéliennes Ordinaires sur un Corps Fini. Inven. Math.8, 238-243 (1969) · Zbl 0179.26201 · doi:10.1007/BF01406076
[6] Davenport, H. Hasse, H.: Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. reine angew. Math.172, 151-182 (1934) · JFM 60.0913.01
[7] Faddeev, D.K.: On the Divisor Class Groups of some Algebraic Curves. Dokl. Tom 136 pp. 296-298 =Sov. Math. Vol.2, No. 1, 67-69 (1961) Faddeev, D.K.: Invariants of Divisor Classes for the Curvesx k (1?x)=y ? in an?-adic Cyclotomic Field. Trudy Mat. (In Russian) Inst. Steklov64, 284-293 (1961) · Zbl 0097.02403
[8] Hasse, H.: Zetafunktion undL-Funktionen zu einem arithmetischen Funktionenkörper vom Fermatschen Typus. Abhand. der Deut. Akad. der Wissen. zu Berlin, 1955 · Zbl 0068.03501
[9] Koblitz, N.:P-adic Variation of the Zeta-Function over Families of Varieties Defined over Finite Fields. Compos. Math.31, 119-218 (1975) · Zbl 0332.14008
[10] Koblitz, N., Rohrlich, D.: Simple Factors in the Jacobian of a Fermat Curve (To appear in Canadian J. of Math.) · Zbl 0399.14023
[11] Mazur, B.: Cohomology of the Fermat Group Scheme. Unpublished manuscript (1977) · Zbl 0358.73009
[12] Oort, F., Tate, J.: Group Schemes of Prime Order. Annales Scient. de l’Ecole Norm. Sup., 4ème Série T.3, fasc. 1, 1-21 (1970) · Zbl 0195.50801
[13] Serre, J.-P.: Lie Algebras and Lie Groups. Benjamin: Reading, 1965 · Zbl 0132.27803
[14] Shimura, G., Taniyama, Y.: Complex Multiplication of Abelian Varieties and its Applications to Number Theory. Tokyo: Math. Soc. Japan 1961 · Zbl 0112.03502
[15] Swinnerton-Dyer, H.P.F.: The Conjectures of Birch and Swinnerton-Dyer, and of Tate. In: Proc. of a Conference on Local Fields. Berlin-Heidelberg-New York: Springer 1967 · Zbl 0197.47101
[16] Tate, J.: Fourier Analysis and Hecke’s Zeta-function. In: J.W. Cassels and A. Fröhlich, Algebraic Number Theory. Proc. of the Brighton Conference, pp. 305-347. New York: Academic Press 1968
[17] Tate, J.: Local Constants. In: A. Fröhlich, Algebraic Numberfields, Prof. of the Durham Conference, 89-133. New York: Academic Press 1977
[18] Weil, A.: Number of Solutions of Equations in Finite Fields. Bull. AMS55, 497-508 (1949) · Zbl 0032.39402 · doi:10.1090/S0002-9904-1949-09219-4
[19] Weil, A.: Jacobi Sums as Grössencharaktere. Trans. AMS73, 487-495 (1952) · Zbl 0048.27001
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