Abstract. For primes p ≥ 7, we give a parametrization of the filtered φ-modules attached to the p-adic Tate modules of abelian surfaces over Q_p with supersingular good reduction. We use this classification to determine the neutral components of the monodromy groups of the associated p-adic representations up to \bar Q_p-isomorphism. Furthermore, we analyze the p-adic distribution of these groups in the moduli space of filtered φ-modules. In particular, we prove that the neutral components are generically isomorphic to GL_2 ×det GL_2.

Abstract. For fixed Hodge data, we construct a finite locally closed refinement of the Wintenberger-type partition on the moduli stack of p-torsion Fontaine–Laffaille modules using Hilbert polynomials. We define line-degree spectra for finite flat commutative p-torsion group schemes over O_{C_p} and finite free Breuil–Kisin–Fargues modules. For p>2, we recover the Wintenberger type of a Fontaine–Laffaille module over the integers of a finite unramified extension of Q_p, with weights in [0,p-2], from the associated BKF spectrum.