Arithmetic of diagonal hypersurfaces over finite fields /

Arithmetic of diagonal hypersurfaces over finite fields /

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Bibliographic Details
Author / Creator:	Gouvêa, Fernando Q. (Fernando Quadros)
Imprint:	Cambridge ; New York : Cambridge University Press, 1995.
Description:	1 online resource (xi, 169 pages) : illustrations.
Language:	English
Series:	London Mathematical Society lecture note series ; 209 London Mathematical Society lecture note series ; 209.
Subject:	Hypersurfaces. Finite fields (Algebra) Finite fields (Algebra) Hypersurfaces. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11181102

Hidden Bibliographic Details
Other authors / contributors:	Yui, Noriko.
ISBN:	9781107362239 1107362237 9780511526060 0511526067 0521498341 9780521498340
Notes:	Includes bibliographical references (pages 163-166) and index. Print version record.
Summary:	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.
Other form:	Print version: Gouvêa, Fernando Q. (Fernando Quadros). Arithmetic of diagonal hypersurfaces over finite fields. Cambridge ; New York : Cambridge University Press, 1995 0521498341

Table of Contents:

1. Twisted Jacobi sums
2. Cohomology groups of V = V[actual symbol not reproducible](c)
3. Twisted Fermat motives
4. The inductive structure and the Hodge and Newton polygons
5. Twisting and the Picard number
6. "Brauer numbers" of twisted Fermat motives
7. Evaluating Q(V, T) at T = q[superscript -r]
8. The Lichtenbaum-Milne conjecture
9. Remarks, observations and open problems
B How to compute the stable Picard number when m is prime.