eprintid: 14935
rev_number: 14
eprint_status: archive
userid: 557
dir: disk0/00/01/49/35
datestamp: 2013-05-16 05:24:14
lastmod: 2013-05-16 10:42:00
status_changed: 2013-05-16 05:24:14
type: doctoralThesis
metadata_visibility: show
creators_name: Riedel, Andreas
title: On Perrin-Riou's exponential map and reciprocity laws for (phi,Gamma)-modules
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
abstract: Let K / Q_p be a finite Galois extension and D a (phi,Gamma)-module over the Robba ring B and N_dR(D) its associated p-adic differential equation. 

In the first part we give a generalization of the Bloch-Kato exponential map for D using continuous Galois-cohomology groups H^i(G_K, W(D)) for the B-pair W(D) associated to D. We construct a big exponential map Omega_D,h for cyclotomic extensions of K for D in the style of Perrin-Riou extending techniques of Berger, which interpolates the generalized Bloch-Kato exponential maps on the finite levels.

In the second part we extend two definitions for pairings on D and its dual D^*(1) (resp. on N_dR(D) and its dual N_dR(D^*(1))) and prove a generalization of the reciprocity law, which relates these pairings under the big exponential map. 

Finally, we give some results on the determinant associated to Omega_D,h, and formulate an integral version of a determinant conjecture in the semi-stable case. Further, we define i-Selmer groups and show under certain hypothesis a torsion property.
date: 2013
id_scheme: DOI
id_number: 10.11588/heidok.00014935
ppn_swb: 1652370455
own_urn: urn:nbn:de:bsz:16-heidok-149359
date_accepted: 2013-04-30
advisor: HASH(0x561a628b6c40)
language: eng
bibsort: RIEDELANDRONPERRINRI2013
full_text_status: public
citation:   Riedel, Andreas  (2013) On Perrin-Riou's exponential map and reciprocity laws for (phi,Gamma)-modules.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/14935/1/diss%20final.pdf