
PDF, English
Download (2MB)  Terms of use 
Abstract
We prove a version of the conjecture of Fukaya and Kato concerning the existence of padic Lfunctions 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 padic Lfunction 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 padic Lfunction having the interpolation behaviour predicted by Fukaya and Kato (up to a nonconstant sign).
Item Type:  Dissertation 

Supervisor:  Venjakob, Prof. Dr. Otmar 
Date of thesis defense:  8 December 2017 
Date Deposited:  30 Jan 2019 08:48 
Date:  2019 
Faculties / Institutes:  The Faculty of Mathematics and Computer Science > Department of Mathematics 
Subjects:  510 Mathematics 