Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T14:01:10.208Z Has data issue: false hasContentIssue false
  • English
  • Français

The Möbius–Wall congruences for p-adic L-functions of CM elliptic curves

Published online by Cambridge University Press:  11 November 2013

THANASIS BOUGANIS
THANASIS BOUGANIS*
Affiliation:
Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we prove, under a technical assumption, the so-called “Möbius–Wall” congruences between abelian p-adic L-functions of CM elliptic curves. These congruences are the analogue of those shown by Ritter and Weiss for the Tate motive, and offer strong evidences in favor of the existence of non-abelian p-adic L-functions for CM elliptic curves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 1 , January 2014 , pp. 183 - 192
Copyright
Copyright © Cambridge Philosophical Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bouganis, Th.. Non-abelian congruences between special values of L-fucntions of elliptic curves; the CM case. Int. J. Number Theory 7, No. 7 (2011), 1883–1934.CrossRefGoogle Scholar
[2]Bouganis, Th.. Non abelian p-adic L-functions and Eisenstein series of unitary groups; the CM-method, preprint. arXiv:1107.1377v2[math.NT].Google Scholar
[3]Coates, J., Fukaya, T., Kato, K., Sujatha, R. and Venjakob, O.. The GL 2-main conjecture for elliptic curves without complex multiplication. Publ. Math. Inst. Hautes. Études Sci. 101 (2005), no. 1, 163–208.CrossRefGoogle Scholar
[4]Fukaya, T. and Kato, K.. A formulation of conjectures on p-adic zeta functions in non-commutative Iwasawa theory. Proceedings of the St. Petersburg Mathematical Society, vol XII (Providence RI). Amer. Math. Soc. Transl. Ser. 2 vol 219 (2006).Google Scholar
[5]Hara, T.. Iwasawa theory of totally real fields for certain non-commutative p-extensions. J. Number Theory 130 (4), (2010), 1068–1097.CrossRefGoogle Scholar
[6]Harris, M., Li, J.-S. and Skinner, C.. p-adic L-functions for unitary Shimura varieties, I: Construction of the Eisenstein measure. Documenta Math. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 393–464.CrossRefGoogle Scholar
[7]Kakde, M.. Proof of the main conjecture of non-commutative Iwasawa theory of totally real number fields in certain cases. J. Algebraic Geometry 20 (2011), 631–683CrossRefGoogle Scholar
[8]Kakde, M.. Proof of the main conjecture of non-commutative Iwasawa theory of totally real number fields. Invent. Math. DOI 10.1007/s00222-012-0436-x, (2012).Google Scholar
[9]Kato, K.. Iwasawa theory of totally real fields for Galois extensions of Heisenberg type, preprint.Google Scholar
[10]Ritter, J. and Weiss, A.. Congruences between abelian pseudomeasures. Math. Res. Lett. 15 (2008), 715–725.CrossRefGoogle Scholar
[11]Ritter, J. and Weiss, A.. Congruences between abelian pseudomeasures II, preprint. arXiv:1001.2091v1[math.NT].Google Scholar
[12]Venjakob, O.. On the work of Ritter and Weiss in Comparison with Kakde's Approach. Noncommutative Iwasawa Main Conjectures over Totally Real Fields, ed. Coates, J.et al. Springer Proceedings in Mathematics and Statistics, 29 (Springer 2013).Google Scholar