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

Format:

Book

Author/Creator:

Serre, Jean-Pierre, 1926- author.

Series:

Research notes in mathematics ; 11.

Research notes in mathematics ; v. 11

Language:

English

Subjects (All):

Polynomials.

Number theory.

Representations of groups.

Cohomology operations.

Physical Description:

1 online resource (168 p.)

Edition:

1st ed.

Place of Publication:

Boca Raton, Fla. : CRC Press, c2012.

Boca Raton, Fla. : CRC Press, 2012.

Language Note:

English

Summary:

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.

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

Notes:

An AK Peters book.

Includes bibliographical references.

Description based on metadata supplied by the publisher and other sources.

ISBN:

9786613908650

9781040188101

1040188109

9780429067617

0429067615

9781283596206

1283596202

9781466501935

1466501936

OCLC:

773034262