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

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Author/Creator:
Serre, Jean-Pierre, 1926-
Language:
English.
Publication date:
2012
Imprint:
Boca Raton, FL : CRC Press, c2012.
Format:
  • Book
  • ix, 163 p. : ill. ; 24 cm.
Note:
On t.p. "x" is subscript. "An AK Peters book."
Bibliography:
Includes bibliographical references (p. 147-155) and indexes.
Contents:
  • ch. 1. Introduction
  • ch. 2. Examples
  • ch. 3. The Chebotarev density theorem for a number field
  • ch. 4. Review of -adic cohomology
  • ch. 5. Auxiliary results on group representations
  • ch. 6. The -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.
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.
Series:
Research notes in mathematics ; v. 11
Chapman & Hall/CRC research notes in mathematics series.
Subjects:
ISBN:
9781466501928
1466501928

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