© 2004

Arithmetic of Higher-Dimensional Algebraic Varieties

  • Bjorn Poonen
  • Yuri Tschinkel


  • Contributors are all leading speciatlists in this importand and expanding field

  • Tschinkel has history with Birkh?ser Basel


Part of the Progress in Mathematics book series (PM, volume 226)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Expository Articles

    1. Front Matter
      Pages 1-1
    2. Peter Swinnerton-Dyer
      Pages 3-35
    3. Roger Heath-Brown
      Pages 37-42
  3. Research Articles

    1. Front Matter
      Pages 83-83
    2. Victor V. Batyrev, Oleg N. Popov
      Pages 85-103
    3. Niklas Broberg, Per Salberger
      Pages 105-120
    4. Jean-Louis Colliot-Thélène, Philippe Gille
      Pages 121-134
    5. Tom Graber, Joseph Harris, Barry Mazur, Jason Starr
      Pages 141-147
    6. Brendan Hassett, Yuri Tschinkel
      Pages 149-173
    7. Bjorn Poonen, José Felipe Voloch
      Pages 175-184
    8. Wayne Raskind, Victor Scharaschkin
      Pages 185-204
    9. Joseph Shalika, Ramin Takloo-Bighash, Yuri Tschinkel
      Pages 205-233
    10. Peter Swinnerton-Dyer
      Pages 235-257
  4. Back Matter
    Pages 269-287

About this book


One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory.


This text, which focuses on higher-dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry.


Contributors: Batyrev, V.V.; Broberg, N.; Colliot-Thélène, J-L.; Ellenberg, J.S.; Gille, P.; Graber, T.; Harari, D.; Harris, J.; Hassett, B.; Heath-Brown, R.; Mazur, B.; Peyre, E.; Poonen, B.; Popov, O.N.; Raskind, W.; Salberger, P.; Scharaschkin, V.; Shalika, J.; Starr, J.; Swinnerton-Dyer, P.; Takloo-Bighash, R.; Tschinkel, Y.: Voloch, J.F.; Wittenberg, O.


Cohomology Dimension Diophantine approximation Grad algebra algebraic geometry algebraic varieties number theory

Editors and affiliations

  • Bjorn Poonen
    • 1
  • Yuri Tschinkel
    • 2
  1. 1.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA
  2. 2.Mathematisches InstitutGöttingenGermany

Bibliographic information

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"These articles which are written by leading experts make interesting reading and also give the non expert reader an idea of the subject.  In addition there is an extensive index covering the entire volume and a glossary of important notions.  In particular readers who are not specialists in the field may find this very helpful."

---Monatshefte für Mathematik