Arithmetic of diagonal hypersurfaces over finite fields

Author(s)

Bibliographic Information

Arithmetic of diagonal hypersurfaces over finite fields

Fernando Q. Gouvêa, Noriko Yui

（London Mathematical Society lecture note series, 209）

Cambridge University Press, 1995

  • : pbk

Available at  / 72 libraries

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Note

Bibliography: p. 163-166

Includes index

Description and Table of Contents

Description

There is now a large body of theory concerning algebraic varieties over finite fields, and many conjectures exist in this area that are of great interest to researchers in number theory and algebraic geometry. This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields, with special focus on the Tate conjecture and the Lichtenbaum-Milne formula for the central value of the L-function. It combines theoretical and numerical work, and includes tables of Picard numbers. Although this book is aimed at experts, the authors have included some background material to help non-specialists gain access to the results.

Table of Contents

  • 1. Twisted Jacobi sums
  • 2. Cohomology groups of n=nnm(c)
  • 3. Twisted Fermat motives
  • 4. The inductive structure and the Hodge and Newton polygons
  • 5. Twisting and the Picard numbers n=nmn(c)
  • 6. Brauer numbers associated to twisted Jacobi sums
  • 7. Evaluating the polynomials Q(n,T) at T=q-r
  • 8. The Lichtenbaum-Milne conjecture for n=nnm(c)
  • 9. Observations and open problems.

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