Higher adelic programme, adelic Riemann-Roch theorems and the BSD conjecture - Czerniawska, Weronika (2018)
The Birch and Swinnerton-Dyer conjecture is one the most important, still unsolved problem in mathematics, included in the list of the Millennium problems. Ivan Fesenko developed an adelic approach to the study of zeta-functions of elliptic curves in relation to the Conjecture. The method establishes relations between analysis and geometry that were not known before. This thesis presents some contributions to Fesenko's programme as well as places this results inside the whole context.