Lectures on N_X (p)

by Serre, Jean-Pierre

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Title Statements

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

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"--

"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"--

Edition Statements

Publication Date:©2012.

Publication Statements

Publisher(s):CRC Press
Place of Publication:Boca Raton, Fla
Language:eng
Publication Date:©2012.

Notes

Verdement en lot.

Monographies électroniques.

"An AK Peters book."

The Physical Object

Description:1 ressource en ligne (1 texte ̌lectronique)

Edition Identifiers

ISBN:9781466501935, 1466501936
oclc:ocn869597405
LC Classification:QA161.P59

Ch. 1. Introduction -- ch. 2. Examples -- ch. 3. The Chebotarev density theorem for a number field -- ch. 4. Review of ℓ-adic cohomology -- ch. 5. Auxiliary results on group representations -- ch. 6. The ℓ-adic properties of N_X(p) -- ch. 7. The archimedean properties of N_X(p) -- ch. 8. The Sato-Tate conjecture -- ch. 9. Higher dimension : the prime number theorem and the Chebotarev theorem.

Subjects

Cohomology operations Number theory Opérations cohomologiques Polynômes polynomials Représentations de groupes Representations of groups Théorie des nombres