  We discuss the Bisognano-Wichmann property for local Poincar\'e covariant
nets of standard subspaces. We give a sufficient algebraic condition on the
covariant representation ensuring the Bisognano-Wichmann and Duality properties
without further assumptions on the net called modularity condition. It holds
for direct integrals of scalar massive and massless representations. We present
a class of massive modular covariant nets not satisfying the Bisognano-Wichmann
property. Furthermore, we give an outlook in the standard subspace setting on
the relation between the Bisognano-Wichmann property and the Split property.
