  We use a series of N-body simulations of the LCDM cosmology to investigate
the redshift evolution since z=1 of the properties and alignment with the
large-scale structure of haloes in clusters, filaments, sheets and voids. We
find that: (i) Once a rescaling of the halo mass with M*, the mass scale
collapsing at redshift z, is performed, there is no further significant
redshift dependence in the halo properties; (ii) The environment influences
halo shape and formation time at all investigated redshifts for haloes with
masses M<M*; and (iii) There is a significant alignment of both spin and shape
of haloes with filaments and sheets. In detail, at all redshifts up to z=1: a)
Haloes with M<M* tend to be more oblate when located in clusters than in the
other environments; this trend is reversed at higher masses: above about M*,
halos in clusters are typically more prolate than similar massive haloes in
sheets, filaments and voids. b) Haloes with M>M* in filaments spin more rapidly
than similar mass haloes in clusters; haloes in voids have the lowest median
spin parameters; c) Haloes with M<M* tend to be younger in voids and older in
clusters; d) In sheets, halo spin vectors tend to lie within the sheet plane
independent of mass; in filaments, instead, haloes with M<M* tend to spin
parallel to the filament and haloes with M>M* perpendicular to it. For masses
M>M*, the major axis of haloes in filaments and sheets is strongly aligned with
the filament or the sheet. Such halo-LSS alignments may be of importance in
weak lensing analyses of cosmic shear. A question that is opened by our study
is why, in the 0 < z < 1 redshift regime that we have investigated, the mass
scale M* sets roughly the threshold below which the LSS-environment either
begins to affect, or reverses, the properties of dark matter haloes.
