Rigid syntomic regulators and the p-adic L-function of a modular form [Elektronische Ressource] / vorgelegt von Maximilian Niklas

Rigid Syntomic Regulators and the p-adicL-function of a modular formDISSERTATION ZUR ERLANGUNG DES DOKTORGRADESDER NATURWISSENSCHAFTEN (DR. RER. NAT.) AN DER FAKULTAT FUR MATHEMATIK DER UNIVERSITATREGENSBURGvorgelegt vonMaximilian NiklasausRegensburg2010Promotionsgesuch eingereicht am: 3. November 2010Die Arbeit wurde angeleitet von: Prof. Dr. Guido KingsPrufungsaussc huss:Prof. Dr. Helmut Abels (Vorsitzender)Prof. Dr. Guido Kings (1. Gutachter)Prof. Dr. Kenichi Bannai, Keio University, Japan (2. Gutachter)Prof. Dr. Uwe JannsenProf. Dr. Klaus Kunnemann (Ersatzprufer)ContentsIntroduction 5Overview 10Chapter I. Syntomic Eisenstein classes 13Chapter II. The product of syntomic Eisenstein classes 23II.1. Syntomic cup product with coe cients 23II.2. Product structures on modular cohomology groups 28II.3. The product of two Eisenstein classes 41II.4. Rigid cohomology and overconvergent modular forms 45II.5. A theorem of Coleman 47II.6. Rigid and non-overconvergent forms 49II.7. A formula for the product of two Eisenstein classes 57Chapter III. The rigid realization of modular motives 59III.1. Rigid cohomology and Hecke operators 60III.2. Classical and p-adic modular forms 69III.3. De nition of the linear form l 72f;rigIII.4. Panchishkin’s linear form l 73fIII.5. Comparison of the linear forms. 75Chapter IV. Panchishkin’s measure 77IV.1. Review of p-adic measures 77IV.2. Convolution of Eisenstein measures 79IV.3.