IWASAWA

Iwasawa theory of p-adic Lie extensions

Coordinatore	RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Germany [DE]
Totale costo	500˙000 €
EC contributo	500˙000 €
Programma	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)
Code Call	ERC-2007-StG
Funding Scheme	ERC-SG
Anno di inizio	2008
Periodo (anno-mese-giorno)	2008-07-01   -   2013-06-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG  Organization address address: SEMINARSTRASSE 2 city: HEIDELBERG postcode: 69117 contact info Titolo: Dr. Nome: Norbert Cognome: Huber Email: send email Telefono: +49 6221 542157 Fax: +49 6221 543599	DE (HEIDELBERG)	hostInstitution	0.00
2	RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG  Organization address address: SEMINARSTRASSE 2 city: HEIDELBERG postcode: 69117 contact info Titolo: Prof. Nome: Otmar Cognome: Venjakob Email: send email Telefono: -551869 Fax: +49-6221-54 5769	DE (HEIDELBERG)	hostInstitution	0.00

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 Obiettivo del progetto (Objective)

'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.'