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Iwasawa theory of p-adic Lie extensions

Ziel

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.

Wissenschaftliches Gebiet

CORDIS klassifiziert Projekte mit EuroSciVoc, einer mehrsprachigen Taxonomie der Wissenschaftsbereiche, durch einen halbautomatischen Prozess, der auf Verfahren der Verarbeitung natürlicher Sprache beruht.

Aufforderung zur Vorschlagseinreichung

ERC-2007-StG
Andere Projekte für diesen Aufruf anzeigen

Gastgebende Einrichtung

RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG
EU-Beitrag
€ 500 000,00
Adresse
SEMINARSTRASSE 2
69117 Heidelberg
Deutschland

Auf der Karte ansehen

Region
Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis
Aktivitätstyp
Higher or Secondary Education Establishments
Hauptforscher
Otmar Venjakob (Prof.)
Links
Gesamtkosten
Keine Daten

Begünstigte (1)