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Coleman maps and the p-adic regulator
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Lei, Antonio, Loeffler, David and Zerbes, Sarah Livia (2011) Coleman maps and the p-adic regulator. Algebra & Number Theory, 5 (8). pp. 1095-1131. doi:10.2140/ant.2011.5.1095 ISSN 1937-0652.
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Official URL: http://dx.doi.org/10.2140/ant.2011.5.1095
Abstract
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Number theory, p-adic numbers, Forms, Modular, Homology theory, Galois cohomology, Algebraic fields | ||||
Journal or Publication Title: | Algebra & Number Theory | ||||
Publisher: | Mathematical Sciences Publishers | ||||
ISSN: | 1937-0652 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | 5 | ||||
Number: | 8 | ||||
Number of Pages: | 37 | ||||
Page Range: | pp. 1095-1131 | ||||
DOI: | 10.2140/ant.2011.5.1095 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 21 January 2016 | ||||
Date of first compliant Open Access: | 21 January 2016 | ||||
Funder: | Australian Research Council (ARC), Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | DP1092496, EP/F04304X/1, EP/F043007/1 |
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