IWASAWA
Iwasawa theory of p-adic Lie extensions
| Coordinatore | RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
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
| # | ||||
|---|---|---|---|---|
| 1 |
RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Organization address
address: SEMINARSTRASSE 2 contact info |
DE (HEIDELBERG) | hostInstitution | 0.00 |
| 2 |
RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
Organization address
address: SEMINARSTRASSE 2 contact info |
DE (HEIDELBERG) | hostInstitution | 0.00 |
Mappa
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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.'