Skip to main content
SpringerLink
Log in
Book cover

Noncommutative Geometry and Number Theory pp 179–185Cite as

The non-abelian (or non-linear) method of Chabauty

  • Chapter

Part of the book series: Aspects of Mathematics ((ASMA))

Abstract

This article is a brief introduction to the ideas surrounding the non-linear Albanese map that provides an approach to Diophantine finiteness theorems in the spirit of the method of Chabauty.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Besser, Amnon Coleman integration using the Tannakian formalism. Math. Ann. 322 (2002), no. 1, 19–48.

    Article  MATH  MathSciNet  Google Scholar 

  2. Chabauty, Claude, Sur les points rationnels des courbes algébriques de genre supérieur l’unité. C. R. Acad. Sci. Paris 212, (1941). 882–885.

    MATH  MathSciNet  Google Scholar 

  3. Coleman, Robert F. Effective Chabauty. Duke Math. J. 52 (1985), no. 3, 765–770.

    Article  MATH  MathSciNet  Google Scholar 

  4. Deligne, Pierre Le groupe fondamental de la droite projective moins trois points. Galois groups over ℚ (Berkeley, CA, 1987), 79–297, Math. Sci. Res. Inst. Publ., 16, Springer, New York, 1989.

    Google Scholar 

  5. Fox, Ralph H. Free differential calculus. I. Derivation in the free group ring. Ann. of Math. (2) 57, (1953). 547–560.

    Article  MathSciNet  Google Scholar 

  6. Hain, Richard M. Higher Albanese manifolds. Hodge theory (Sant Cugat, 1985), 84–91, Lecture Notes in Math., 1246, Springer, Berlin, 1987.

    Google Scholar 

  7. Jannsen, Uwe On the l-adic cohomology of varieties over number fields and its Galois cohomology. Galois groups over ℚ (Berkeley, CA, 1987), 315–360, Math. Sci. Res. Inst. Publ., 16, Springer, New York, 1989.

    Google Scholar 

  8. Kim, Minhyong The motivic fundamental group of P 1 \ {0, 1,∞} and the theorem of Siegel. Inventiones Mathematicae (to be published).

    Google Scholar 

  9. Ochi, Yoshihiro; Venjakob, Otmar On the ranks of Iwasawa modules over p-adic Lie extensions. Math. Proc. Cambridge Philos. Soc. 135 (2003), no. 1, 25–43.

    Article  MATH  MathSciNet  Google Scholar 

  10. Vologodsky, Vadim Hodge structure on the fundamental group and its application to p-adic integration. Mosc. Math. J. 3 (2003), no. 1, 205–247, 260.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Arizona, Tucson, AZ, 85721

    Minhyong Kim

Authors
  1. Minhyong Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD, 21218, USA

    Caterina Consani

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn

    Matilde Marcolli

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Friedr. Vieweg & Sohn Verlag ∣ GWV Fachverlage GmbH, Wiesbaden

About this chapter

Cite this chapter

Kim, M. (2006). The non-abelian (or non-linear) method of Chabauty. In: Consani, C., Marcolli, M. (eds) Noncommutative Geometry and Number Theory. Aspects of Mathematics. Vieweg. https://doi.org/10.1007/978-3-8348-0352-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation