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The arithmetic of Fermat curves

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References

  1. Bosch, S., Guntzer, U., Remmert, R.: Non-archimedean analysis. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  2. Carlitz, L.: A generalization of Maillet's determinant and a bound for the first factor of the class number. Proc. Am. Math. Soc.12, 256–261 (1961)

    Google Scholar 

  3. Cassels, J.W.S., Fröhlich, A. (eds.): Algebraic number theory. London: Academic Press 1967

    Google Scholar 

  4. Coleman, R.F.: Torsion points on curves andp-adic abelian integrals. Ann. Math.121, 111–168 (1983)

    Google Scholar 

  5. Coleman, R.F.: Effective chabauty. Duke Math. J.52, 765–770 (1985)

    Article  Google Scholar 

  6. Coleman, R.F., McCallum, W.G.: Stable reduction of Fermat curves and Jacobi sum Hecke characters. Crelle

  7. Eichler, M.: Eine Bemerkung zur Fermatschen Vermutung. Acta Arith.11, 129–131, 261 (1965)

    Google Scholar 

  8. 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)

    Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. Kummer, E.: Beweis des Fermatschen Satzes der Unmöglichkeit vonx λ+y λ=z λ für eine unendliche Anzahl Primzahlen λ. Collected Papers, I, pp. 274–281 (1847)

    Google Scholar 

  11. McCallum, W.G.: The degenerate fiber of the Fermat curve. In: Koblitz, N. (ed.) Number theory related to Fermat's last theorem. Boston: Birkhäuser 1982

    Google Scholar 

  12. McCallum, W.G.: On the Shafarevich-Tate group of the jacobian of a quotient of the Fermat curve. Invent. Math.93, 637–666 (1988)

    Article  Google Scholar 

  13. Ribenboim, P.: 13 lectures on Fermat's last theorem. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  14. Ribet, K.: A modular construction of unramifiedp-extensions of511-1. Invent. Math.34, 151–162 (1976)

    Article  Google Scholar 

  15. Serre, J.-P.: Local fields. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  16. Washington, L.C.: Introduction to cyclotomic fields. Berlin Heidelberg New York: Springer 1982

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA

    William G. McCallum

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  1. William G. McCallum
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This research was supported in part by National Science Foundation grant DMS-9002095

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McCallum, W.G. The arithmetic of Fermat curves. Math. Ann. 294, 503–511 (1992). https://doi.org/10.1007/BF01934338

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