Zeta and L-Functions of Varieties and Motives

by Bruno Kahn

Overview

The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.

Product Details

ISBN-13:	9781108703390
Publisher:	Cambridge University Press
Publication date:	05/07/2020
Series:	London Mathematical Society Lecture Note Series , #462
Pages:	214
Product dimensions:	5.98(w) x 8.90(h) x 0.51(d)

About the Author

Bruno Kahn is Directeur de recherche at CNRS. He has written around 100 research papers in areas including algebraic and arithmetic geometry, algebraic K-theory and the theory of motives.

Table of Contents

Introduction; 1. The Riemann zeta function; 2. The zeta function of a Z-scheme of finite type; 3. The Weil Conjectures; 4. L-functions from number theory; 5. L-functions from geometry; 6. Motives; Appendix A. Karoubian and monoidal categories; Appendix B. Triangulated categories, derived categories, and perfect complexes; Appendix C. List of exercises; Bibliography; Index.

Editorial Reviews

‘The book will be of interest to both young mathematicians and physicists as well as experienced scholars.’ Nikolaj M. Glazunov, zbMATH Open

From the Publisher