Skip to main content

Overconvergent p-adic Siegel modular forms

  • Chapter
Algebra and Number Theory
  • 756 Accesses

Abstract

We give a construction of overconvergent p-adic Siegel modular forms and canonical subgroups using rigid analytic geometry.

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 66.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. P. Berthelot: Cohomologie rigide et cohomologie rigide à supports propre. Première partie, Prépublication IRM 96–08 , 91 pages, 1996.

    Google Scholar 

  2. S. Bosch, W. Lütkebohmert, M. Raynaud: Formal and rigid geometry, I Math. Ann. 295 (1993) 291–317, II Math. Ann. 296 (1993) 403–429, III Math.Ann. 302 (1995) 1–29.

    Article  MathSciNet  MATH  Google Scholar 

  3. C-L. Chai: Compactification of Siegel moduli scheme, Cambridge Univ. Press, Cambridge, 1985.

    Book  MATH  Google Scholar 

  4. Robert F. Coleman: Classical and overconvergent modular forms, Invent. Math. 124 (1996), no. 1–3, 215–241.

    Article  MathSciNet  MATH  Google Scholar 

  5. Robert F. Coleman: p-adic Banach spaces and families of modular forms. Invent. Math. 127 (1997), no. 3, 417–479.

    Article  MathSciNet  MATH  Google Scholar 

  6. R.F. Coleman, B. Mazur: The eigencurve, Galois representations in arithmetic algebraic geometry (Durham), 1–113, London Math. Soc. Lecture Note Ser., 254, Cambridge Univ. Press, Cambridge, 1998.

    Google Scholar 

  7. G. Faltings, C-L. Chai: Degeneration of abelian varieties, Ergebnisse der Mathematik 22 Springer 1990.

    Book  MATH  Google Scholar 

  8. F.Q. Gouvêa: Arithmetic of p-adic Modular Forms, Lecture Notes in Math. 1304 Springer 1988.

    MATH  Google Scholar 

  9. H. Hida: p-adic Hecke algebras for GL2over totally real fields, Ann. of Math. 128:2 (1988) 295–384.

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Hida: Control theorems of coherent sheaves on Shimura varieties of PEL type, J. Inst. Math. Jussieu 1 (2002) 1–76.

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Katz: Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Inst. Hautes Etudes Sci, 39 (1970) 175–232.

    Article  MathSciNet  MATH  Google Scholar 

  12. N. Katz: p-adic properties of modular forms, in Modular functions of one variable, Springer Lecture Notes in Math. 350, 69–190, 1973.

    Chapter  Google Scholar 

  13. N. Katz: p-adic L functions for CM fields, Invent. Math. 49 (1978) 199–297.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Kisin, K.F. Lai: Overconvergent Hilbert modular forms, preprint 2003.

    MATH  Google Scholar 

  15. W. Lütkebohmert: Formal-algebraic and rigid analytic geometry, Math. Ann. 286 (1990) 341–371.

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Mumford, J. Fogarty, F. Kirwan: Geometric invariant theory. Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (2) 34. Springer-Verlag, Berlin, 1994.

    Book  MATH  Google Scholar 

  17. J-P. Serre: Formes modulaires et fonctions zta p-adiques in Modular functions of one variable, III pp. 191–268. Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973.

    Chapter  Google Scholar 

  18. R.L. Taylor: On congruence between modular forms, Princeton PHD Dissertation, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Hindustan Book Agency

About this chapter

Cite this chapter

Lai, K.F., Zhao, C.L. (2005). Overconvergent p-adic Siegel modular forms. In: Tandon, R. (eds) Algebra and Number Theory. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-23-1_17

Download citation

Publish with us

Policies and ethics