References
Altman, A., Kleiman, S.: Introduction to Grothendieck duality theory. (Lecture Notes in Mathematics, Vol. 146). Berlin-Heidelberg-New York: Springer 1970
Bosch, S., Lütkebohmert, W.: Stable reduction and uniformization of abelian varieties I. Math. Ann.270, 349–379 (1985)
Bosch, S., Guntzer, U., Remmert, R.: Non-archimedean analysis. Berlin-Heidelberg-New York: Springer 1984
Cassels, J.W.S., Fröhlich, A.: Algebraic number theory. London: Academic Press 1967
Faddeev, D.K.: Invariants of divisor classes for the curvesx k(1−x)=y l in anl-adic cyclotomic field. Tr. Mat. Inst. Steklova64, 284–293 (1961)
Fresnel, J., Put, M., van der: Géometrie analytique rigide et applications Boston: Birkhäuser 1981
Greenberg, R.: On the Jacobian variety of some algebraic curves. Compos. Math.42, 345–359 (1981)
Gross, B.H., Rohrlich, D.E.: Some results on the Mordell-Weil group of the jacobian of the Fermat curve. Invent. Math.44, 201–224 (1978)
Grothendieck, A., Dieudonné, J.: Eléments de Géometrie Algébrique III. Étude cohomologique des faisceaux cohérents. Publ. Math. Inst. Hautes Etud. Sci.11 (1961);17 (1963)
Hartshorne, R.: Algebraic geometry. Berlin-Heidelberg-New York: Springer 1977
Hartshorne, R.: Residues and duality. (Lecture Notes in Mathematics, Vol. 20). Berlin-Heidelberg-New York: Springer 1966
Johnson, W.: On the vanishing of the Iwasawa invariant μ forp<8,000. Math. Comp.27, 387–396 (1973)
Lang, S.: Reciprocity and correspondences. Am. J. Math.80, 431–440 (1958)
Lang, S., Tate, J.: Principal homogeneous spaces over abelian varieties. Am. J. Math.80, 659–685 (1958)
Lichtenbaum, S.: Curves over discrete valuation rings. Am. J. Math.85, 380–405 (1968)
McCallum, W.G.: The degenerate fiber of the Fermat curve. Number theory related to Fermat's last theorem, Neal Koblitz (ed.). Boston: Birkhäuser 1982
Milne, J.S.: Arithmetic duality theorems. London: Academic Press 1986
Milne, J.S.: Jacobian varieties. Arithmetic Geometry, Cornell, G., Silverman, J.H. (eds.). Berlin-Heidelberg-New York: Springer 1986
Mumford, D.: Abelian varieties. Oxford: Oxford University Press 1970
Raynaud, M.: Spécialisation du foncteur de Picard. Publ. Math., Inst. Hautes Etud. Sci.38, 27–76 (1970)
Serre, J-P.: Groupes algébriques et corps de classes. Paris: Hermann 1959
Serre, J-P.: Local fields. Translation of corps locaux. Paris: Hermann, 1959. Berlin-Heidelberg-New York: Springer 1979
Vandiver, H.S.: A property of cyclotomic integers and its relation to Fermat's last theorem. Ann. Math.21, 73–80 (1919–1920)
Wagstaff, S.: The irregular primes to 125,000. Math. Comp.32, 583–591 (1978)
Washington L.C.: Introduction to cyclotomic fields. Berlin-Heidelberg-New York: Springer 1982
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McCallum, W.G. On the Shafarevich-Tate group of the jacobian of a quotient of the Fermat curve. Invent Math 93, 637–666 (1988). https://doi.org/10.1007/BF01410203
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DOI: https://doi.org/10.1007/BF01410203