Another look at the Dwork family

Research output: Chapter in Book/Report/Conference proceedingChapter

11 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages89-126
Number of pages38
DOIs
StatePublished - Jan 1 2009

Publication series

NameProgress in Mathematics
Volume270
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Dwork family
  • Fourier Transform
  • Hypergeometric
  • Kloosterman sheaf
  • Monodromy

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  • Cite this

    Katz, N. M. (2009). Another look at the Dwork family. In Progress in Mathematics (pp. 89-126). (Progress in Mathematics; Vol. 270). Springer Basel. https://doi.org/10.1007/978-0-8176-4747-6_4