# SIMBa: A walk through the Birch and Swinnerton-Dyer conjecture

El proper dimecres, 4 de novembre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Resum: The Birch and Swinnerton-Dyer conjecture is one of the seven millennium problems posed by the Clay Mathematics Institute. There have been many different approaches along the last decades, but it still remains open. The conjecture relates the rank of an elliptic curve with the order of vanishing of a complex $L$-function, and it has been proved when the latter is at most one. At this point, there is a natural question posed by Mazur, Tate and Teitelbaum during the eighties: why dowe look at the complex $L$-function? What about the $L$-functions attached to other non-archimedian completions of the rational numbers? This question will move us to the $p$-adic world, where new phenomen aappear, leading us to suggestive points of view about the conjecture
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