Pseudo-modularity and Iwasawa theory

Wake, Preston; Wang-Erickson, Carl

doi:10.1353/ajm.2018.0022

Cited by 14 publications

(24 citation statements)

References 32 publications

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“…As well as proving these new results, we review the most novel parts of [WWE15]. In this way, this note may serve as an introduction to [WWE15].…”

Section: Preston Wake and Carl Wang-ericksonmentioning

confidence: 90%

“…This allows for the definition of an ordinary pseudorepresentation of G Q , which we extend to non-field coefficients. We overview this and other background from [WWE15] in § §2 and 3.…”

Section: Preston Wake and Carl Wang-ericksonmentioning

confidence: 99%

“…This section is a brief synopsis of § §2, 3, and 6 of [WWE15]. We overview background information from Iwasawa theory and ordinary Λ-adic Hecke algebras and modular forms.…”

Section: Background: Iwasawa Theory and Hecke Algebrasmentioning

confidence: 99%

“…In this note, we show that the methods of [WWE15] can be extended to the whole Eisenstein component H, provided that we make stronger assumptions on class groups. Namely, we have to assume that the plus-part X + of the Iwasawa class group of the relevant cyclotomic field vanishes.…”

Section: Introductionmentioning

confidence: 96%

“…The key technical innovation behind our previous work [WWE15] was our definition of an ordinary 2-dimensional pseudorepresentation of G Q = Gal(Q/Q). Using this notion, we were able to study ordinary Galois deformations in the case where the residual representation is reducible.…”

Section: Introductionmentioning

confidence: 99%

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Ordinary pseudorepresentations and modular forms

Wake

Wang-Erickson

2017

Proc. Amer. Math. Soc. Ser. B

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Abstract. In this note, we observe that the techniques of our paper "Pseudomodularity and Iwasawa theory" can be used to provide a new proof of some of the residually reducible modularity lifting results of Skinner and Wiles. In these cases, we have found that a deformation ring of ordinary pseudorepresentations is equal to the Eisenstein local component of a Hida Hecke algebra. We also show that Vandiver's conjecture implies Sharifi's conjecture.

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“…As well as proving these new results, we review the most novel parts of [WWE15]. In this way, this note may serve as an introduction to [WWE15].…”

Section: Preston Wake and Carl Wang-ericksonmentioning

confidence: 90%

“…This allows for the definition of an ordinary pseudorepresentation of G Q , which we extend to non-field coefficients. We overview this and other background from [WWE15] in § §2 and 3.…”

Section: Preston Wake and Carl Wang-ericksonmentioning

confidence: 99%

“…This section is a brief synopsis of § §2, 3, and 6 of [WWE15]. We overview background information from Iwasawa theory and ordinary Λ-adic Hecke algebras and modular forms.…”

Section: Background: Iwasawa Theory and Hecke Algebrasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Ordinary pseudorepresentations and modular forms

Wake

Wang-Erickson

2017

Proc. Amer. Math. Soc. Ser. B

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Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

Wang-Erickson

2017

Math. Ann.

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We construct and study the moduli of continuous representations of a profinite group with integral p -adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is algebraizable. When this profinite group is the absolute Galois group of a p -adic local field, we show that these moduli spaces admit Zariski-closed loci cutting out Galois representations that are potentially semi- stable with bounded Hodge-Tate weights and a given Hodge and Galois type. As a consequence, we show that these loci descend to the universal deformation ring of the corresponding pseudorepresentation

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New criteria for Vandiver’s conjecture using Gauss sums – Heuristics and numerical experiments

Gras¹

2020

Proc Math Sci

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Pseudo-modularity and Iwasawa theory

Cited by 14 publications

References 32 publications

Ordinary pseudorepresentations and modular forms

Ordinary pseudorepresentations and modular forms

Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

New criteria for Vandiver’s conjecture using Gauss sums – Heuristics and numerical experiments

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