Skip to main content

On the Structure of Selmer Groups

  • Conference paper
  • First Online:
Elliptic Curves, Modular Forms and Iwasawa Theory (JHC70 2015)

Abstract

Our objective in this paper is to prove a rather broad generalization of some classical theorems in Iwasawa theory.

Dedicated to John Coates

Research supported in part by National Science Foundation grant DMS-0200785.

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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

References

  1. Bruns, W., Herzog, J.: Cohen–Macaulay Rings, Cambridge Studies in Advanced Math, vol. 39. Cambridge University Press (1998)

    Google Scholar 

  2. Cohen, I.S.: On the structure and ideal theory of complete local rings. Trans. Am. Math. Soc. 59, 54–106 (1946)

    Article  MathSciNet  MATH  Google Scholar 

  3. Greenberg, R.: Iwasawa theory for \(p\)-adic representations. Adv. Stud. Pure Math. 17, 97–137 (1989)

    MathSciNet  MATH  Google Scholar 

  4. Greenberg, R.: Iwasawa theory and \(p\)-adic deformations of motives. Proc. Symp. Pure Math. 55(II), 193–223 (1994)

    Google Scholar 

  5. Greenberg, R.: Iwasawa theory for elliptic curves. Lect. Notes Math. 1716, 51–144 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. Greenberg, R.: On the structure of certain Galois cohomology groups, Documenta Math. Extra Volume Coates, 357–413 (2006)

    Google Scholar 

  7. Greenberg, R.: Surjectivity of the global-to-local map defining a Selmer group. Kyoto J. Math. 50, 853–888 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Greenberg, R.: Iwasawa theory for \({Z}^m_p\)-extensions, in preparation

    Google Scholar 

  9. Greenberg, R.: Iwasawa theory—past and present. Adv. Stud. Pure Math. 30, 335–385 (2001)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ralph Greenberg .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Greenberg, R. (2016). On the Structure of Selmer Groups. In: Loeffler, D., Zerbes, S. (eds) Elliptic Curves, Modular Forms and Iwasawa Theory. JHC70 2015. Springer Proceedings in Mathematics & Statistics, vol 188. Springer, Cham. https://doi.org/10.1007/978-3-319-45032-2_6

Download citation

Publish with us

Policies and ethics