  This paper treats a number of issues of the cuprates, ranging from the spin
resonance peak and the linear one-particle scattering rate to the
superconducting transition, in the frame of a Fermi liquid model. Recent ARPES
expts. by Valla et al., Science vol. 285, 2110 (1999), and e-print
cond-mat/0003407, directly support the linearity of the one-particle scattering
rate everywhere in the Brillouin zone we obtained here. We show that the origin
of this linearity is the strong linear in energy term of the imaginary part of
the carrier susceptibility. This result yields directly a linear in temperature
resistivity and linear in 1/energy optical conductivity. We show that the low
energy dependence of the susceptibility can have a purely fermionic origin. We
introduce an antiferromagnetic ansatz for the susceptibility of the
carriers.Inter alia, this ansatz may explain the appearance of the spin
resonance peak (observed in neutron scattering) in the normal state of the
cuprates. Further, we obtain particularly high transition temperatures $T_c$
from our Eliashberg scheme by using this ansatz: we have a $d_{x^2-y^2}$ gap
with $T_c > 120 ^o$K for nearest neighbour hopping $t=250meV$.
