Objetivo The goal of this project is to extend the work of Beilinson-Bloch-Esnault (BBE) on de Rahm epsilon-factors in dimension one to higher local fields. Together with my collaborators Oliver Braunling and Jesse Wolfson we have carefully studied one of the main tools of BBE, Tate vector bundles, in an abstract context which allows to handle higher-dimensional situations. Moreover, we have successfully constructed a special case of higher epsilon-factors, called higher-dimensional Contou-Carrère symbols, and established an array of reciprocity laws for this case. It seems very likely that similar methods, also of K-theoretic nature like in the case of symbols, can be used to shed light on higher de Rahm epsilon-factors, and reciprocity phenomena thereof. The candidate will investigate the connection between the approach via Tate objects, and extend Patel's K-theoretic framework in a compatible way. A higher analogue of Beilinson's topological epsilon-factors is also envisioned, and a comparison result between this theory and the de Rham version. This project offers a new viewpoint on the arithmetic and geometric behaviour of higher local fields. Ámbito científico natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesphysical sciencesclassical mechanicsnatural sciencesmathematicspure mathematicsarithmeticsprime numbersnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Palabras clave Epsilon-factors flat connections holonomic D-modules higher local fields Tate vector spaces K-theory reciprocity adèles Programa(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Tema(s) MSCA-IF-2015-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Convocatoria de propuestas H2020-MSCA-IF-2015 Consulte otros proyectos de esta convocatoria Régimen de financiación MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinador FREIE UNIVERSITAET BERLIN Aportación neta de la UEn € 159 460,80 Dirección KAISERSWERTHER STRASSE 16-18 14195 Berlin Alemania Ver en el mapa Región Berlin Berlin Berlin 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 € 159 460,80
