L-invariants of Tate Curves

Hida, Haruzo

doi:10.4310/pamq.2009.v5.n4.a6

Cited by 14 publications

(10 citation statements)

References 23 publications

(1 reference statement)

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“…Combining the above comparison of L-invariants with [18], Theorem 5.7, yields the following partial answer to Hida's exceptional zero conjecture (cf. [15]). where q A,p is the Tate period of A at p ∈ S p (A) and e p (A) = e(π p , 1) is the modified Euler factor at p ∈ S p − S p (A).…”

Section: Discussionmentioning

confidence: 99%

Functoriality of automorphic L-invariants and applications

Gehrmann

2017

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We study the behaviour of automorphic L-Invariants associated to cuspidal representations of GL(2) of cohomological weight 0 under abelian base change and Jacquet-Langlands lifts to totally definite quaternion algebras.Under a standard non-vanishing hypothesis on automorphic L-functions and some technical restrictions on the automorphic representation and the base field we get a simple proof of the equality of automorphic and arithmetic L-invariants. This together with Spieß' results on p-adic L-functions yields a new proof of the exceptional zero conjecture for modular elliptic curves -at least, up to sign.

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Section: Discussionmentioning

confidence: 99%

Functoriality of automorphic L-invariants and applications

Gehrmann

2017

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“…The L-invariant of an elliptic curve E /Q is studied by Mazur-Tate-Teitelbaum [19] and Greenberg-Stevens [7]. Hida studied the L-invariants of Tate curves [14] [15] and make a vast generalization of Mazur-Tate-Teitelbaum conjecture to the symmetric powers of Galois representations associated to Hilbert modular forms [16], which gave explicit predictions of the L-invariants of these representations. Hida proved certain cases of this conjecture, assuming a conjectural shape of certain universal deformation rings over characteristic zero fields.…”

Section: Characteristic Zero Deformation and L-invariantmentioning

confidence: 99%

Framed Deformation of Galois Representation

Chen

2008

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We studied framed deformations of two dimensional Galois representation of which the residue representation restrict to decomposition groups are scalars, and established a modular lifting theorem for certain cases. We then proved a family version of the result, and used it to determine the structure of deformation rings over characteristic zero fields. As a corollary, we obtain the L-invariant of adjoint square representation associated to a Hilbert Hecke eigenform.

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“…In [15] Hida formulated a generalization of this exceptional zero conjecture. To state it we let F be a totally real field, and let f be a Hilbert modular form of parallel weight 2 over F .…”

Section: Introduction 1exceptional Zero Phenomenon For Cyclotomic Z P...mentioning

confidence: 99%