Lei, Antonio, Loeffler, David and Zerbes, Sarah Livia. (2011) Coleman maps and thep-adic regulator. Algebra & Number Theory, Vol.5 (No.8). pp. 1095-1131. ISSN 1937-0652

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Algebra & Number Theory
Publisher:	Mathematical Sciences Publishers
ISSN:	1937-0652
Date:	2011
Volume:	Vol.5
Number:	No.8
Number of Pages:	37
Page Range:	pp. 1095-1131
Identification Number:	10.2140/ant.2011.5.1095
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	ARC, EPSRC
Grant number:	DP1092496, EP/F04304X/1, EP/F043007/1
URI:	http://wrap.warwick.ac.uk/id/eprint/48532

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