The Iwasawa Main Conjectures for ${\rm GL}_2$ and derivatives of $p$-adic $L$-functions

Castella, Francesc; Wan, Xin

doi:10.48550/arxiv.2001.03878

Cited by 1 publication

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“…Castella-Wan [CW20] proved similar results assuming that the global root number for f /K is −1, complementing [SU14] (again assuming that the prime p splits in K/Q).…”

Section: )mentioning

confidence: 62%

Semi-ordinary Iwasawa theory for Rankin--Selberg products

Büyükboduk¹,

Lei²

2020

Preprint

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Chapter 1. Introduction 1.1. The setting 1.2. Conjectures and Results 1.3. A summary of our results 1.4. Layout 1.5. Notation Chapter 2. Construction of the optimized Coleman maps 2.1. Dieudonné modules and ϕ-eigenvectors 2.2. Factorization of one-variable Perrin-Riou maps 2.3. Two-variable Perrin-Riou maps and Coleman maps 2.4. The case a p (g) = 0 Chapter 3. Beilinson-Flach elements and p-adic L-functions 3.1. Beilinson-Flach elements 3.2. Euler systems of rank 2 and uniform integrality 3.3. p-adic L-functions Chapter 4. Selmer groups and main conjectures 4.1. Definitions of Selmer groups 4.2. Classical and signed Iwasawa main conjectures Chapter 5. Applications towards main conjectures 5.1. Cyclotomic main conjectures for f ⊗ g 5.2. Cyclotomic main conjectures for f ⊗ g 5.3. Main conjectures over an imaginary quadratic field where p is inert Appendix A. A divisibility criterion in regular rings Appendix B. p-adic Rankin-Selberg L-functions and universal deformations B.1. The set up B.2. The minimally ramified universal deformation representation B.3. Hida families B.4. p-adic Rankin-Selberg L-function Appendix C. Images of Galois representations attached to Rankin-Selberg convolutions C.1. Group theory C.2. Applications to families on GL 2 × Res K/Q GL 1

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“…Castella-Wan [CW20] proved similar results assuming that the global root number for f /K is −1, complementing [SU14] (again assuming that the prime p splits in K/Q).…”

Section: )mentioning

confidence: 62%

Semi-ordinary Iwasawa theory for Rankin--Selberg products

Büyükboduk¹,

Lei²

2020

Preprint

View full text Add to dashboard Cite

show abstract

The Iwasawa Main Conjectures for ${\rm GL}_2$ and derivatives of $p$-adic $L$-functions

Cited by 1 publication

References 20 publications

Semi-ordinary Iwasawa theory for Rankin--Selberg products

Semi-ordinary Iwasawa theory for Rankin--Selberg products

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