Partial Bloch--Kato Selmer groups of $B$-pairs as delta functors

In this article we revisit the partial Selmer groups introduced by Ding in cohomological degree one. On the subcategory of partially de Rham positive $B$-pairs we extend them to higher cohomological degree and show that the resulting groups form a cohomological delta functor satisfying a variant of the Euler--Poincaré characteristic formula and Tate duality.