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Title of Journal: Invent math

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Abbravation: Inventiones mathematicae

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Springer Berlin Heidelberg

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10.1016/0020-7381(81)80103-9

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1432-1297

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Image of Emphasis Type="Italic"Λ/Emphasisadic

Authors: Haruzo Hida
Publish Date: 2012/12/04
Volume: 194, Issue: 1, Pages: 1-40
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Abstract

Let p≥5 be a prime If an irreducible component of the spectrum of the ‘big’ ordinary Hecke algebra does not have complex multiplication under mild assumptions we prove that the image of its mod p Galois representation contains an open subgroup of Open image in new window for the canonical “weight” variable T This fact appears to be deep as it is almost equivalent to the vanishing of the μinvariant of the Kubota–Leopoldt padic Lfunction and the anticyclotomic Katz padic Lfunction Another key ingredient of the proof is the anticyclotomic main conjecture proven by Rubin/Mazur–TilouineThe author is partially supported by the NSF grant DMS 0753991 and DMS 0854949 and part of this work was done during the author’s stay in January to March 2010 at the Institut Henri Poincaré—Centre Emile Borel The author thanks this institution for hospitality and support

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Other Papers In This Journal:
  1. Serre’s modularity conjecture (I)
  2. Serre’s modularity conjecture (I)
  3. Erratum to: Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space
  4. Representation theory of $\mathcal{W}$-algebras
  5. The Kodaira dimension of the moduli of K3 surfaces
  6. Brownian Gibbs property for Airy line ensembles
  7. Degree formula for connective K -theory
  8. Some quantitative results in $${\mathcal {C}}^0$$ symplectic geometry
  9. Convexes divisibles IV : Structure du bord en dimension 3
  10. The classification of irreducible admissible mod p representations of a p -adic GL n
  11. Some prime factorization results for type II 1 factors
  12. $\mathcal{C}^{2}$ surface diffeomorphisms have symbolic extensions
  13. On the weights of mod p Hilbert modular forms
  14. Operator-algebraic superridigity for SL n (ℤ), n ≥3
  15. Exceptional zero formulae and a conjecture of Perrin-Riou
  16. F-singularities of pairs and Inversion of Adjunction of arbitrary codimension
  17. Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case
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