  It is commonly believed that nonuniform Berry curvature destroys the
Girvin-MacDonald-Platzman algebra and as a consequence destabilizes fractional
Chern insulators. In this work we disprove this common lore by presenting a
theory for all topological ideal flatbands with nonzero Chern number C. The
smooth single-particle Bloch wavefunction is proved to admit an exact
color-entangled form as a superposition of C lowest Landau level type
wavefunctions distinguished by boundary conditions. Including repulsive
interactions, Abelian and non-Abelian model fractional Chern insulators of
Halperin type are stabilized as exact zero-energy ground states no matter how
nonuniform Berry curvature is, as long as the quantum geometry is ideal and the
repulsion is short-ranged. The key reason behind is the existence of an
emergent Hilbert space in which Berry curvature can be exactly flattened by
adjusting wavefunction's normalization. In such space, the flatband-projected
density operator obeys a closed Girvin-MacDonald-Platzman type algebra, making
exact mapping to C-layered Landau levels possible. In the end we discuss
applications of the theory to moire flatband systems with a particular focus on
the fractionalized phase and spontaneous symmetry breaking phase recently
observed in graphene based twisted materials.
