Obiettivo One of the most challenging topics in modern number theory is the mysterious relation between special values of L-functions and Galois cohomology: they are the “shadows” in the two completely different worlds of complex and p-adic analysis of one and the same geometric object, viz the space of solutions for a given diophantine equation over the integral numbers, or more generally a motive M. The main idea of Iwasawa theory is to study manifestations of this principle such as the class number formula or the Birch and Swinnerton Dyer Conjecture simultaneously for whole p-adic families of such motives, which arise e.g. by considering towers of number fields or by (Hida) families of modular forms. The aim of this project is to supply further evidence for I. the existence of p-adic L-functions and for main conjectures in (non-commutative) Iwasawa theory, II. the (equivariant) epsilon-conjecture of Fukaya and Kato as well as III. the 2-variable main conjecture of Hida families. In particular, we hope to construct the first genuine “non-commutative” p-adic L-function as well as to find (non-commutative) examples fulfilling the expectation that the epsilon-constants, which are determined by the functional equations of the corresponding L-functions, build p-adic families themselves. In the third item a systematic study of Lie groups over pro-p-rings and Big Galois representations is planned with applications to the arithmetic of Hida families. Campo scientifico natural sciencesmathematicspure mathematicsmathematical analysisfunctional equationsnatural sciencesmathematicspure mathematicsarithmeticsL-functionsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Parole chiave Coleman map Iwasawa theory K-theory L-functions motives p-adic representations Programma(i) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Argomento(i) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Invito a presentare proposte ERC-2007-StG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-SG - ERC Starting Grant Istituzione ospitante RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG Contributo UE € 500 000,00 Indirizzo SEMINARSTRASSE 2 69117 Heidelberg Germania Mostra sulla mappa Regione Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Otmar Venjakob (Prof.) Contatto amministrativo Norbert Huber (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG Germania Contributo UE € 500 000,00 Indirizzo SEMINARSTRASSE 2 69117 Heidelberg Mostra sulla mappa Regione Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Otmar Venjakob (Prof.) Contatto amministrativo Norbert Huber (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato