De Sitter, gravitino mass and the swampland

Abstract: In this contribution, we review a general argument showing that de Sitter critical points of extended supergravity are in tension with the magnetic weak gravity conjecture if the gravitino mass is vanishing. Motivated by this assumption, we review then the gravitino conjecture, which states that the limit of vanishing gravitino mass is pathological for the effective field theory description. Finally, we discuss more in general the fate of de Sitter critical points (with massless gravitini) in supergravity and comment on extensions of these works along various directions. Part of the material here presented is unpublished.