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

• Applicant: Professor Dr. Werner Bley
• Subject Area: Mathematics
• Term: from 2010 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 171229853

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 Programme: Priority Programmes
• Subproject of: SPP 1489: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory