Vol. 11, No. 8, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author index
To appear
Other MSP journals
$\mathfrak{p}$-rigidity and Iwasawa $\mu$-invariants

Ashay A. Burungale and Haruzo Hida

Vol. 11 (2017), No. 8, 1921–1951

Let F be a totally real field with ring of integers O and p be an odd prime unramified in F. Let p be a prime above p. We prove that a mod p Hilbert modular form associated to F is determined by its restriction to the partial Serre–Tate deformation space G ̂m Op (p-rigidity). Let KF be an imaginary quadratic CM extension such that each prime of F above p splits in K and λ a Hecke character of K. Partly based on p-rigidity, we prove that the μ-invariant of the anticyclotomic Katz p-adic L-function of λ equals the μ-invariant of the full anticyclotomic Katz p-adic L-function of λ. An analogue holds for a class of Rankin–Selberg p-adic L-functions. When λ is self-dual with the root number  1, we prove that the μ-invariant of the cyclotomic derivatives of the Katz p-adic L-function of λ equals the μ-invariant of the cyclotomic derivatives of the Katz p-adic L-function of λ. Based on previous works of the authors and Hsieh, we consequently obtain a formula for the μ-invariant of these p-adic L-functions and derivatives. We also prove a p-version of a conjecture of Gillard, namely the vanishing of the μ-invariant of the Katz p-adic L-function of λ.

Hilbert modular Shimura variety, Hecke stable subvariety, Iwasawa $\mu$-invariant, Katz $p$-adic L-function
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 19F27
Received: 26 September 2016
Revised: 21 November 2016
Accepted: 6 February 2017
Published: 15 October 2017
Ashay A. Burungale
Département de Mathématiques
Institute Galilée
Université Paris 13
93430 Villetaneuse
Haruzo Hida
Department of Mathematics
Los Angeles, CA 90095-1555
United States