  In a previous article we introduced various moduli stacks of two-dimensional
tamely potentially Barsotti-Tate representations of the absolute Galois group
of a p-adic local field, as well as related moduli stacks of Breuil-Kisin
modules with descent data. We study the irreducible components of these stacks,
establishing in particular that the components of the former are naturally
indexed by certain Serre weights.
