Zeta and L-functions of varieties and motives
著者
書誌事項
Zeta and L-functions of varieties and motives
（London Mathematical Society lecture note series, 462）
Cambridge University Press, 2020
- : pbk
- タイトル別名
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Fonctions zêta et L de variétés et de motifs
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注記
"Originally published in French as Fonctions zêta et L de variétés et de motifs by Calvage et Mounet in 2018"--T.p. verso
Includes bibliographical references (p. 197-206) and index
内容説明・目次
内容説明
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.
目次
- 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.
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