Towards a Formulation of the Birch and Swinnerton-Dyer Conjecture for Abelian Schemes Over Varieties Over Finite Fields

Watch a 51-minute mathematics lecture from the 1st Brazilian Workshop in Analytic Number Theory where Professor Amilcar Pacheco from UFRJ explores potential formulations of the Birch and Swinnerton-Dyer conjecture for abelian schemes over varieties defined over finite fields. Learn about recent developments in Number Theory while connecting with the broader context of mathematical advances, including Zhang and Maynard's work on prime gaps and Viazovska's breakthrough in sphere packing. Delivered at IMPA (Instituto de Matemática Pura e Aplicada) in Rio de Janeiro, the talk contributes to a larger initiative bringing together Number Theory researchers from across Brazil to foster collaboration and showcase current mathematical research in the country.