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.
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 10 mm
Gewicht
ISBN-13
978-0-521-49834-0 (9780521498340)
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Schweitzer Klassifikation
Autor*in
Colby College, Maine
Queen's University, Ontario
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.
