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Other titles in the London Mathematical Society Lecture Notes series:
Arithmetic of Diagonal Hypersurfaces Over Finite Fields (London Mathematical Society Lecture Note)by Fernando Q. Gouvea
Synopses & ReviewsPublisher Comments:There is now a large body of theory concerning algebraic varieties over finite fields, and many conjectures in this area are of great interest to researchers in number theory and algebraic geometry. This book deals with the arithmetic of diagonal hypersurfaces over finite fields, with special focus on the Tate conjecture and the LichtenbaumMilne formula for the central value of the Lfunction. 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 nonspecialists gain access to the results.
Synopsis:Focusing on the Tate conjecture and the LichtenbaumMilne formula for the central value of the Lfunction, this book is about the arithmetic of diagonal hypersurfaces over finite fields. It combines theoretical and numerical work and includes tables of Picard numbers.
Synopsis:This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields.
Description:Includes bibliuographical references (p. 163166) and index.
Table of Contents1. 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=qr; 8. The LichtenbaumMilne conjecture for n=nnm(c); 9. Observations and open problems.
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