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The hodge conjecture for Fermat varieties

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References

  1. Borevich, Z.I., Shafarevich, I.R.: Number theory. New York, London: Academic Press 1966

    Google Scholar 

  2. Deligne, P., Katz, N.: Groupes de monodromie en géométrie algébrique (SGA 7 II). Lecture Notes in Mathematics, Vol.340. Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  3. Grothendieck, A.: Cohomologiel-adique et fonctionsL (SGA 5). Lecture Notes in Mathematics, Vol.589. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  4. Grothendieck, A.: Hodge's general conjecture is false for trivial reasons. Topology8, 299–303 (1969)

    Google Scholar 

  5. Hodge, W.V.D.: The topological invariants of algebraic varieties. Proc. Int. Congr. Math. 181–192 (1950)

  6. Katz, N.: On the intersection matrix of a hypersurface. Ann. Sci. École Norm. Sup.2, 583–598 (1969)

    Google Scholar 

  7. Kawai, S.: A note on Steenrod reduced powers of algebraic cocycles, In: Complex analyses and algebraic geometry, pp. 375–381. Tokyo and Cambridge: Iwanami and Cambridge University Press, 1977

    Google Scholar 

  8. Ogus, A.: Griffiths transversality in crystalline cohomology. Ann. Math.108, 395–419 (1978)

    Google Scholar 

  9. Ran, Z.: Cycles on Fermat hypersurfaces (preprint)

  10. Sasakura, N.: On some results on the Picard numbers of certain algebraic surfaces. J. Math. Soc. Jpn.20, 297–321 (1968)

    Google Scholar 

  11. Shioda, T., Katsura, T.: On Fermat varieties. Tôhoku Math. J.31, 97–115 (1979)

    Google Scholar 

  12. Shioda, T.: The Hodge Conjecture and the Tate Conjecture for Fermat varieties. Proc. Japan Academy55, 111–114 (1979)

    Google Scholar 

  13. Tate, J.: Algebraic cycles and poles of zeta functions. In: Arithmetical algebraic geometry, pp. 93–110. New York: Harper and Row, 1965

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Tokyo, Japan

    Tetsuji Shioda

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  1. Tetsuji Shioda
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Shioda, T. The hodge conjecture for Fermat varieties. Math. Ann. 245, 175–184 (1979). https://doi.org/10.1007/BF01428804

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