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We establish a geometrisation of the Breuil-M\'ezard conjecture forpotentially Barsotti-Tate representations, as well as of the weight part ofSerre's conjecture, for moduli stacks of two-dimensional mod p representationsof the absolute Galois group of a p-adic local field.

The geometric Breuil-M\'ezard conjecture for two-dimensional potentially Barsotti-Tate Galois representations