Coleman maps and the p-adic regulator

Details Coleman maps and the p-adic regulator Coleman maps and the p-adic regulator

2010-06-26

arxiv.org/abs/1006.5163v2

Mathematics

Number Theory

27 pages

Scientific paper

This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman maps for a crystalline representation of the Galois group of Qp with nonnegative Hodge-Tate weights. In this paper, we study these Coleman maps using Perrin-Riou's p-adic regulator L_V. Denote by H(\Gamma) the algebra of Qp-valued distributions on \Gamma = Gal(Qp(\mu (p^\infty) / Qp). Our first result determines the H(\Gamma)-elementary divisors of the quotient of D_{cris}(V) \otimes H(\Gamma) by the H(\Gamma)-submodule generated by (\phi * N(V))^{\psi = 0}, where N(V) is the Wach module of V. By comparing the determinant of this map with that of L_V (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.

Affiliated with

Also associated with

No associations

Rating

Coleman maps and the p-adic regulator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Coleman maps and the p-adic regulator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coleman maps and the p-adic regulator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-630322