title: A p-adic L-function  with canonical motivic periods  for families of modular forms
creator: Fütterer, Michael
subject: ddc-510
subject: 510 Mathematics
description: 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
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserver/25983/1/diss.pdf
identifier: DOI:10.11588/heidok.00025983
identifier: urn:nbn:de:bsz:16-heidok-259833
identifier:   Fütterer, Michael  (2019) A p-adic L-function with canonical motivic periods for families of modular forms.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/25983/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng