Skip to main content

Potential Automorphy of Odd-Dimensional Symmetric Powers of Elliptic Curves and Applications

  • Chapter
  • First Online:
Book cover Algebra, Arithmetic, and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 270))

Summary

I explain how to prove potential automorphy for odd-dimensional symmetric power L-functions.

2000 Mathematics Subject Classifications: 11F80, 11F70, 11G05, 11R37, 22E55

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Arthur, L. Clozel, Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Annals of Mathematics Studies 120 (1989).

    Google Scholar 

  2. L. Clozel, Motifs et formes automorphes: applications du principe de fonctorialité, in L. Clozel and J. S. Milne, eds., Automorphic Forms, Shimura Varieties, and L-functions, New York: Academic Press (1990), Vol I, 77–160.

    Google Scholar 

  3. L. Clozel, Représentations Galoisiennes associées aux représentations automorphes autoduales de GL (n), Publ. Math. I.H.E.S., 73, 97–145 (1991).

    MATH  MathSciNet  Google Scholar 

  4. L. Clozel, On the cohomology of Kottwitz’s arithmetic varieties, Duke Math. J., 72 (1993) 757–795.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Clozel, M. Harris, R. Taylor, Automorphy for some ℓ-adic lifts of automorphic mod ℓ Galois representations, Publ. Math. I.H.E.S., 108 (2008) 1–181.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Clozel, J.-P. Labesse, Changement de base pour les représentations cohomologiques de certains groupes unitaires, in [L], 119–133.

    Google Scholar 

  7. M. Harris, Construction of automorphic Galois representations, manuscript (2006); draft of article for Stabilisation de la formule des traces, variétés de Shimura, et applications arithmétiques, Book 3.

    Google Scholar 

  8. M. Harris, N. Shepherd-Barron, R. Taylor, A family of Calabi-Yau varieties and potential automorphy, Annals of Math. (in press).

    Google Scholar 

  9. M. Harris, R. Taylor, The geometry and cohomology of some simple Shimura varieties, Annals of Math. Studies, 151 (2001).

    Google Scholar 

  10. R. Kottwitz, On the λ-adic representations associated to some simple Shimura varieties, Invent. Math., 108, 653–665 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  11. J.-P. Labesse, Cohomologie, stabilisation et changement de base, Astérisque, 257 (1999).

    Google Scholar 

  12. J.-P. Serre, Abelian ℓ-adic representations and elliptic curves, New York: Benjamin (1968).

    Google Scholar 

  13. F. Shahidi, On certain L-functions, Am. J. Math., 103 (1981) 297–355.

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Taylor, Automorphy for some ℓ-adic lifts of automorphic mod ℓ Galois representations, II, Publ. Math. I.H.E.S., 108 (2008) 183–239.

    MATH  Google Scholar 

  15. R. Taylor, Remarks on a conjecture of Fontaine and Mazur, J. Inst. Math. Jussieu, 1 (2002) 1–19.

    Article  MathSciNet  Google Scholar 

  16. R. Taylor, T. Yoshida, Compatibility of local and global Langlands correspondences, J.A.M.S., 20 (2007), 467–493.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Harris .

Editor information

Editors and Affiliations

Additional information

To Yuri Ivanovich Manin

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Harris, M. (2009). Potential Automorphy of Odd-Dimensional Symmetric Powers of Elliptic Curves and Applications. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_1

Download citation

Publish with us

Policies and ethics