eprintid: 25983
rev_number: 14
eprint_status: archive
userid: 4241
dir: disk0/00/02/59/83
datestamp: 2019-01-30 08:48:36
lastmod: 2019-01-30 09:49:48
status_changed: 2019-01-30 08:48:36
type: doctoralThesis
metadata_visibility: show
creators_name: Fütterer, Michael
title: A p-adic L-function
with canonical motivic periods
for families of modular forms
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
abstract: We prove a version of the conjecture of Fukaya and Kato concerning the existence of p-adic L-functions for motives in the case of certain Hida families of modular forms and for commutative towers of fields, the novelty being the exact accordance with the conjectural interpolation formula. To do so, we first calculate the expressions in their conjectural formula as explicitly as possible and compare the result to the interpolation formula of the p-adic L-function constructed by Kitagawa. Here we use Eichler-
Shimura isomorphisms to relate the periods appearing in Fukaya’s and Kato’s formula to the error terms appearing in Kitagawa’s formula, which are defined in terms of modular symbols. Under a technical hypothesis on the Hida family we show that the conjectural interpolation formula differs
from Kitagawa’s one only by a unit in the Iwasawa algebra, so we find a p-adic L-function having the interpolation behaviour predicted by Fukaya and Kato (up to a non-constant sign).
date: 2019
id_scheme: DOI
id_number: 10.11588/heidok.00025983
ppn_swb: 1653764333
own_urn: urn:nbn:de:bsz:16-heidok-259833
date_accepted: 2017-12-08
advisor: HASH(0x55e83b36a6d8)
language: eng
bibsort: FUTTERERMIAPADICLFUN2019
full_text_status: public
citation:   Fütterer, Michael  (2019) A p-adic L-function with canonical motivic periods for families of modular forms.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/25983/1/diss.pdf