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. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisfunctional equationsnatural sciencesmathematicspure mathematicsarithmeticsL-functionsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Keywords Coleman map Iwasawa theory K-theory L-functions motives p-adic representations Programme(s) 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) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2007-StG See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG EU contribution € 500 000,00 Address SEMINARSTRASSE 2 69117 Heidelberg Germany See on map Region Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis Activity type Higher or Secondary Education Establishments Principal investigator Otmar Venjakob (Prof.) Administrative Contact Norbert Huber (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG Germany EU contribution € 500 000,00 Address SEMINARSTRASSE 2 69117 Heidelberg See on map Region Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis Activity type Higher or Secondary Education Establishments Principal investigator Otmar Venjakob (Prof.) Administrative Contact Norbert Huber (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data