zbMATH — the first resource for mathematics

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

14G25 Global ground fields in algebraic geometry
14G05 Rational points
14H25 Arithmetic ground fields for curves
14H40 Jacobians, Prym varieties
Full Text: DOI EuDML
[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 Unpublished manuscript (1977) · Zbl 0358.73009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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.