Objetivo 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. Ámbito científico natural sciencesmathematicspure mathematicsmathematical analysisfunctional equationsnatural sciencesmathematicspure mathematicsarithmeticsL-functionsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Palabras clave Coleman map Iwasawa theory K-theory L-functions motives p-adic representations Programa(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) Tema(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Convocatoria de propuestas ERC-2007-StG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG Aportación de la UE € 500 000,00 Dirección SEMINARSTRASSE 2 69117 Heidelberg Alemania Ver en el mapa Región Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis Tipo de actividad Higher or Secondary Education Establishments Investigador principal Otmar Venjakob (Prof.) Contacto administrativo Norbert Huber (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG Alemania Aportación de la UE € 500 000,00 Dirección SEMINARSTRASSE 2 69117 Heidelberg Ver en el mapa Región Baden-Württemberg Karlsruhe Heidelberg, Stadtkreis Tipo de actividad Higher or Secondary Education Establishments Investigador principal Otmar Venjakob (Prof.) Contacto administrativo Norbert Huber (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
