de Sitter Extrema and the Swampland

Recently it has been conjectured that string theory does not allow for dS vacua or dS extrema. To scrutinize such a conjecture, it is important to study concrete string theory compactifications and spell out their assumptions and potential shortcomings. We do so for one particular class of string compactifications, namely classical compactifications of type II string theory with fluxes, D-branes and O-planes on manifolds with SU(3) structure. In particular, we revisit previously found dS critical points, construct many new ones and check whether they invalidate the dS swampland conjecture.