Iwasawa theory for modular forms at supersingular primes
By Antonio Lei. Compositio Mathematica, 2009
61 citations recorded by the source corpus.
Abstract We generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of the plus and minus Coleman maps for normalised new forms of arbitrary weights and relate Pollack’s p-adic L-functions to the plus and minus Selmer groups. In addition, by generalising works of Pollack and Rubin on CM elliptic curves, we prove the ‘main conjecture’ for CM modular forms.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/23b098f3ed6c30cce31d1fa1dbd8c55f55fb7905
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Citations in the corpus
- Coleman maps and the p-adic regulator (2010, background): “Our assumption on the eigenvalues of ϕ allows us to define the Perrin-Riou pairing Li = L1,(1+π)⊗νi,1 : H 1 Iw(Qp, Vf̄ (k − 1))→ H(Γ) for i = 1, 2 where we have identified Vf (1) ∗(1) with Vf̄ (k−1) (see [Lei09, Section 3.2] or [LLZ10, Section 3.3] for details).”
- Wach modules and Iwasawa theory for modular forms (2009, methodology): “Hence, we can identify the kernels described in Corollary 5.15 with ker(Col±) described in [Lei09] via the isomorphism h1Iw,Vf̄ (k−1): Proposition 5.16.”