Arithmetic of Diagonal Hypersurfaces over Finite Fields [Paperback]

This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields.Focusing on the Tate conjecture and the Lichtenbaum-Milne formula for the central value of the L-function, this book is about the arithmetic of diagonal hypersurfaces over finite fields. It combines theoretical and numerical work and includes tables of Picard numbers.Focusing on the Tate conjecture and the Lichtenbaum-Milne formula for the central value of the L-function, this book is about the arithmetic of diagonal hypersurfaces over finite fields. It combines theoretical and numerical work and includes tables of Picard numbers.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 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 nonspecialists gain access to the results.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 LichtenbaumMilne conjecture for n=nnm(c); 9. Observations and open problems.