2005
DOI: 10.1007/s00222-005-0467-7
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Variation of Iwasawa invariants in Hida families

Abstract: Let r : G_Q -> GL_2(Fpbar) be a p-ordinary and p-distinguished irreducible residual modular Galois representation. We show that the vanishing of the algebraic or analytic Iwasawa mu-invariant of a single modular form lifting r implies the vanishing of the corresponding mu-invariant for all such forms. Assuming that the mu-invariant vanishes, we also give explicit formulas for the difference in the algebraic or analytic lambda-invariants of modular forms lifting r. In particular, our formula shows that the lamb… Show more

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Cited by 108 publications
(184 citation statements)
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“…We note that some authors, e.g. [EPW06] Proof. Since the image ofρ F in GL 2 (F) has order prime to p, we can consider its Teichmüller lift ρ to GL 2 (W (F)) where W (F) are the Witt vectors of F. Such a representation is necessarily split on G p (it is ordinary, hence reducible on G p , and since it is a finite image characteristic zero representation, it is semisimple on G p ).…”
Section: Families Of Exceptional Typementioning
confidence: 97%
See 1 more Smart Citation
“…We note that some authors, e.g. [EPW06] Proof. Since the image ofρ F in GL 2 (F) has order prime to p, we can consider its Teichmüller lift ρ to GL 2 (W (F)) where W (F) are the Witt vectors of F. Such a representation is necessarily split on G p (it is ordinary, hence reducible on G p , and since it is a finite image characteristic zero representation, it is semisimple on G p ).…”
Section: Families Of Exceptional Typementioning
confidence: 97%
“…Denote by T new N its new-quotient which acts on the space of Λ-adic ordinary cuspforms of tame level N which are N -new. Hida constructed (see [H85], [EPW06]) a continuous representation:…”
Section: Ordinary Hecke Algebrasmentioning
confidence: 99%
“…We will be concerned with comparing the Selmer groups of two congruent Galois representations. Over the cyclotomic Z p -extension, such studies were carried out in [EPW,G94,GV,Ha]. One of the motivation behind these studies lies in the philosophy that the "Iwasawa main conjecture" should be preserved by congruences.…”
Section: Introductionmentioning
confidence: 99%
“…These results were extended to arbitrary modular forms over Q in [3]. The methods given in this paper are a generalization of those of [3] to arbitrary algebraic groups and number fields.…”
mentioning
confidence: 96%
“…The case of F = Q, G = GL 2 and r the identity is studied via Hida theory in [3]. The work of [4] and [8] provide additional cases where we can apply our results.…”
mentioning
confidence: 99%