Modular forms in characteristic ℓ
 and special values of their L
-functions

Ash, Avner; Stevens, Glenn

doi:10.1215/s0012-7094-86-05346-9

Cited by 92 publications

(155 citation statements)

References 22 publications

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“…The first part follows from Lemmas 4.1 and 4.3. The rest of the Corollary follows once one knows the isomorphism σ r /Y ∼ = σ s (r), which follows from Lemma 3.2(a) and (c) of [AS86].…”

Section: The Kernel Of the Mapmentioning

confidence: 96%

Explicit Reduction Modulo p of Certain Two-Dimensional Crystalline Representations

Buzzard

Gee

2009

International Mathematics Research Notices

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“…The first part follows from Lemmas 4.1 and 4.3. The rest of the Corollary follows once one knows the isomorphism σ r /Y ∼ = σ s (r), which follows from Lemma 3.2(a) and (c) of [AS86].…”

Section: The Kernel Of the Mapmentioning

confidence: 96%

Explicit Reduction Modulo p of Certain Two-Dimensional Crystalline Representations

Buzzard

Gee

2009

International Mathematics Research Notices

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“…Then ρ arises with weight 2 and level Nl when ∈ 2 ( 1 (Nl), χ g ). By Theorem 3.5 of [1] we have that (g) where k = g + 2.…”

Section: Proposition 1 a Modular Representation ρ Arises With Weightmentioning

confidence: 97%

“…This follows from Edixhoven's theorem on the minimality of the weight (Theorem 4.5 of [4]). Now using Theorem 3.5 of [1] we have that…”

Section: Lemma 1 If ρ Is Modular Arising From S K(ρ) (N(ρ)) Then Thementioning

confidence: 99%

“…The notation is the same used in the article [1]. Let H denote the classical Hecke algebra, which acts on the space M k ( 1 (N)) of weight k modular forms over 1 (N).…”

Section: Lemma 1 If ρ Is Modular Arising From S K(ρ) (N(ρ)) Then Thementioning

confidence: 99%

“…For k 2 let k ( 1 (N)) be the systems of eigenvalues : H →F l occurring inM k ( 1 (N)), the space of mod l modular forms of weight k (see [1] for the precise definition).…”

Section: Lemma 1 If ρ Is Modular Arising From S K(ρ) (N(ρ)) Then Thementioning

confidence: 99%

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Untitled

Figueiredo

1999

Compositio Mathematica

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Abstract. We study an analog over an imaginary quadratic field K of Serre's conjecture for modular forms. Given a continuous irreducible representation ρ: Gal(Q/K) → GL 2 (F l ) we ask if ρ is modular. We give three examples of representations ρ obtained by restriction of even representations of Gal(Q/Q). These representations appear to be modular when viewed as representations over K, as shown by the computer calculations described at the end of the paper.Mathematics Subject Classifications (1991): 11F30, 11F67, 11F11, 11R32.

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