The Eigencurve

Coleman, Robert F.; Mazur, Barry

doi:10.1017/cbo9780511662010.003

Cited by 118 publications

(149 citation statements)

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“…Coleman and Mazur [8] showed for tame level 1, and Kisin [12] for arbitrary tame level eigencurve, that the non-critical classical points are smooth and étale over the weight space, provided α = β (which is conjectured and known for k = 2). For k > 2, Bellaïche and Chenevier [3] proved that the critical Eisenstein series E critp k is a smooth point which is étale over the weight space.…”

Section: Introductionmentioning

confidence: 93%

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Geometry of the eigencurve at critical Eisenstein series of weight 2

Majumdar¹

2015

J. Théor. Nombres Bordeaux

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In this paper we show that the critical Eisenstein series of weight 2, E critp 2, is smooth in the eigencurve C(l), where l is a prime. We also show that E critp,ord l 2 is smooth in the full eigencurve C f ull (l) and E critp,ord l 1 ,ord l 2 2 is non-smooth in the full eigencurve C f ull (l 1 l 2 ). Further, we show that, E critp 2, is étale over the weight space in the eigencurve C(l). As a consequence, we show that level lowering conjecture of Paulin fails to hold at E critp,ord l 2 is étale over the weight space in C(ℓ) 9

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Section: Introductionmentioning

confidence: 93%

“…Coleman and Mazur [8] introduced a rigid analytic curve C parametrizing finite slope overconvergent p-adic eigenforms of tame level 1, called eigencurve. This was axiomatized and generalized by Buzzard [7] to all levels.…”

Section: Introductionmentioning

confidence: 99%

Geometry of the eigencurve at critical Eisenstein series of weight 2

Majumdar¹

2015

J. Théor. Nombres Bordeaux

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“…Dans [3], Buzzard a axiomatisé la construction de [5] et [6]. Sa "machine" permet d'associer une variété de Hecke à la donnée (A, M, H, U p ) à condition de vérifier que M satisfait une hypothèse (Pr) que nous allons rappeler.…”

Section: La Théorie Spectraleunclassified

Overconvergent modular forms

Pilloni¹

2013

Ann. inst. Fourier

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“…For instance, there are several constructions that start with the p-adic representations associated to classical modular forms (which do have a geometric origin), and produce new p-adic representations by p-adic interpolation. These constructions include the p-adic families of Hida [11], and the eigencurve of Coleman and Mazur [5]. (Note that these are global representations, so one has to first restrict to a decomposition group to view them within our framework.…”

Section: Setup and Overviewmentioning

confidence: 99%

Some new directions in p-adic Hodge theory

Kedlaya¹

2009

J. Théor. Nombres Bordeaux

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We recall some basic constructions from p-adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B-pairs, introduced recently by Berger, which provides a natural enlargement of the category of p-adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology, including Tate local duality, extends to B-pairs.

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The Eigencurve

Cited by 118 publications

References 0 publications

Geometry of the eigencurve at critical Eisenstein series of weight 2

Geometry of the eigencurve at critical Eisenstein series of weight 2

Overconvergent modular forms

Some new directions in p-adic Hodge theory

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