Lectures on N_X (p) / Jean-Pierre Serre.

Author
Serre, Jean-Pierre, 1926 [Browse]
Format
Book
Language
English
Published/​Created
Boca Raton, Fla. : CRC Press, 2012.
Description
1 online resource (168 p.)

Details

Subject(s)
Series
Summary note
  • This book presents several basic techniques in algebraic geometry, group representations, number theory, -adic and standard cohomology, and modular forms. It explores how NX(p) varies with p when the family (X) of polynomial equations is fixed. The text examines the size and congruence properties of NX(p) and describes the ways in which it is computed. Along with covering open problems and offering simple, illustrative examples, the author presents various theorems, including the Chebotarev density theorem and the prime number theorem-- Provided by publisher.
  • The main topic involves counting solutions mod p of a system of polynomial equations, as p varies. The book is based on a series of lectures presented by the author in Taiwan. Using this idea, Serre visits algebra and number theory and asks some non-standard questions, especially on group representations-- Provided by publisher.
Notes
An AK Peters book.
Bibliographic references
Includes bibliographical references.
Language note
English
Contents
Front Cover; Contents; Preface; Conventions; Chapter 1. Introduction; Chapter 2. Examples; Chapter 3. The Chebotarev Density Theorem for a Number Field; Chapter 4. Review of l-adic Cohomology; Chapter 5. Auxiliary Results on Group Representations; Chapter 6. The l-adic Properties of NX(p); Chapter 7. The Archimedean Properties of NX(p); Chapter 8. The Sato-Tate Conjecture; Chapter 9. Higher Dimension: the Prime Number Theorem and the Chebotarev Density Theorem; References
ISBN
  • 0-429-06761-5
  • 1-283-59620-2
  • 9786613908650
  • 1-4665-0193-6
OCLC
773034262
Doi
  • 10.1201/b11315
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