Objetivo The Birch--Swinnerton-Dyer conjecture, one of the Millennium Prize Problems, is one of the central unsolved problems in mathematics. It predicts a relation between the arithmetic of an elliptic curve and the properties of the L-function of the elliptic curve. Some special cases of the conjecture were proven by Kolyvagin; the main ingredient in his proof is an algebraic construction called an Euler system. Even though Euler systems are extremely powerful tools, so far only five examples are known to exist. I propose to construct several new examples of Euler systems, in order to prove new cases of the Birch--Swinnerton-Dyer conjecture. In particular, I believe the following theorem to be within reach:Let A be either a modular elliptic curve over a (real or imaginary) quadratic number field, or a modular abelian surface over the rational numbers. If the L-value L(A, 1) is non-zero, then the Mordell--Weil group of A is finite (i.e. the Birch--Swinnerton-Dyer conjecture holds for A). Ámbito científico natural sciencescomputer and information sciencescomputer securitycryptographynatural sciencesmathematicspure mathematicsarithmeticsL-functions Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-CoG-2014 - ERC Consolidator Grant Convocatoria de propuestas ERC-2014-CoG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-COG - Consolidator Grant Institución de acogida UNIVERSITY COLLEGE LONDON Aportación neta de la UEn € 1 070 473,00 Dirección GOWER STREET WC1E 6BT London Reino Unido Ver en el mapa Región London Inner London — West Camden and City of London Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 070 473,00 Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo UNIVERSITY COLLEGE LONDON Reino Unido Aportación neta de la UEn € 1 070 473,00 Dirección GOWER STREET WC1E 6BT London Ver en el mapa Región London Inner London — West Camden and City of London Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 070 473,00
