Coleman maps and the p-adic regulator
By Antonio Lei, David Loeffler, Sarah Livia Zerbes. 2010
55 citations recorded by the source corpus.
We study the Coleman maps for a crystalline representation V with non-negative Hodge–Tate weights via Perrin-Riou’s p-adic “regulator” or “expanded logarithm” map ℒV . Denote by ℋ(Γ) the algebra of ℚp-valued distributions on Γ =Gal(ℚp(μp∞)∕ℚp). Our first result determines the ℋ(Γ)-elementary divisors of the quotient of Dcris(V ) ⊗ (Brig,ℚp+)ψ=0 by the ℋ(Γ)-submodule generated by (φ∗ℕ(V ))ψ=0, where ℕ(V ) is the Wach module of V . By comparing the determinant of this map with that of ℒV (which can be computed via Perrin-Riou’s explicit reciprocity law), we obtain a precise description of the images of the Coleman maps. In the case when V arises from a modular form, we get some stronger results about the integral Coleman maps, and we can remove many technical assumptions that were required in our previous work in order to reformulate Kato’s main conjecture in terms of cotorsion Selmer groups and bounded p-adic L-functions.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5d13e14d0fe59ac341a05c3f0c402dc221a72371
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Citations in the corpus
- Wach modules and Iwasawa theory for modular forms (2009, methodology): “In a forthcoming paper [LLZ10], we give a description of the images of the Coli using Perrin-Riou’s p-adic regulator.”