Skip to main content
SpringerLink
Log in

Iwasawa invariants of galois deformations

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Fix a residual ordinary representation :G F →GL n (k) of the absolute Galois group of a number field F. Generalizing work of Greenberg–Vatsal and Emerton–Pollack–Weston, we show that the Iwasawa invariants of Selmer groups of deformations of depends only on and the ramification of the deformation.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. Bloch, S. and Kato, K.: L-functions and Tamagawa numbers of motives. In: The Grothendieck Festschrift, Vol. I, Birkhäuser, Boston, 1990, pp 333–400

  2. Diamond, F. and Taylor, R.: Lifting modular mod l representations. Duke Math. J. 74, 253–269 (1994)

    Article  Google Scholar 

  3. Emerton, M., Pollack, R. and Weston, T.: Variation of Iwasawa invariants in Hida families preprint, 2004, to appear in Invent. Math.

  4. Fujiwara, K.: Deformation rings and Hecke algebras in the totally real case, preprint.

  5. Greenberg, R.: Iwasawa theory for p-adic representations. In: Algebraic number theory, Adv. Stud. Pure Math. 17, Academic Press, Boston, 1989, pp 97–137

  6. Greenberg, R.: Iwasawa theory for elliptic curves. In: Arithmetic theory of elliptic curves (Cetraro, 1997), Lecture Notes in Math. 1716, Springer, Berlin, 1999, pp 51–144

  7. Greenberg, R. and Vatsal, V.: On the Iwasawa invariants of elliptic curves. Invent. Math. 142, 17–63 (2000)

    Article  Google Scholar 

  8. Hida, H.: Adjoint Selmer groups as Iwasawa modules. Israel J. of Math. 120, 361–427 (2000)

    Google Scholar 

  9. Livne, R.: On the conductors of mod ℓ Galois representations coming from modular forms. J. Number Theory 31, 133–141 (1989)

    Article  Google Scholar 

  10. Perrin-Riou, B.: Représentations p-adiques ordinaires. In: Périodes p-adiques (Bures-sur-Yvette, 1988), Asterisque 223, 185–200 (1994)

  11. Tilouine, J.: Deformations of Galois representations and Hecke algebras, Narosa Publishing House, Delhi, 1996

  12. Tilouine, J. and Urban, E.: Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations. Ann. Sci. École Norm. Sup. 32, 499–574 (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003-9305, USA

    Tom Weston

Authors
  1. Tom Weston
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tom Weston.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weston, T. Iwasawa invariants of galois deformations. manuscripta math. 118, 161–180 (2005). https://doi.org/10.1007/s00229-005-0575-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-005-0575-0

Keywords

Search

Navigation