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Another Look at the Dwork Family

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Algebra, Arithmetic, and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 270))

Summary

We give a new approach to the cohomology of the Dwork family, and more generally of single-monomial deformations of Fermat hypersurfaces. This approach is based on the surprising connection between these families and Kloosterman sums, and makes use of the Fourier Transform and the theory of Kloosterman sheaves and of hypergeometric sheaves.

2000 Mathematics Subject Classifications: 14D10, 14D05, 14C30, 34A20

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Authors and Affiliations

  1. Princeton University, Mathematics, Fine Hall, NJ, 08544-1000, USA

    Nicholas M. Katz

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  1. Nicholas M. Katz
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Correspondence to Nicholas M. Katz .

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Editors and Affiliations

  1. Courant Inst. Mathematical, New York University, Mercer St. 251, New York, 10012, USA

    Yuri Tschinkel

  2. Eberly College of Science, Pennsylvania State University, University Park, 16802, USA

    Yuri Zarhin

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Dedicated to Yuri Manin on his seventieth birthday

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Katz, N.M. (2009). Another Look at the Dwork Family. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_4

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