The Equivariant Tamagawa Number Conjecture for the base change of an abelian variety

Antragsteller Professor Dr. Werner Bley
Fachliche Zuordnung Mathematik
Förderung Förderung von 2010 bis 2015
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 171229853
 

Projektbeschreibung

This project is a complement to the algorithmic part of BL 395/3-1 where the Equivariant Tamagawa Number Conjecture (ETNC) of Burns and Flach is studied in the case of Tate motives. In this new project we want to consider ETNC for the base change of an abelian variety A which is defined over Q. Here ETNC is an equivariant refinement of the famous Birch and Swinnerton-Dyer conjecture. More explicitly, ETNC describes the leading terms of twisted Hasse-Weil-L-functions in terms of cohomological data associated to the motive which is attached to A. The aim of the project is to derive explicit formulations of these equivariant conjectures which makes them amenable to numerical verifications and to develop and implement algorithms in order to provide numerical evidence.
DFG-Verfahren Schwerpunktprogramme
Teilprojekt zu SPP 1489:  Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory