Superconductivity in cuprates, the van Hove scenario

The existence of van Hove singularities close to the Fermi level in all high T-c cuprates has been experimentally established. We develop a theory using these singularities which enables us to compute the main physical properties : T-c, gap and gap anisotropy, specific heat and magnetic susceptibility. All these results agree well with the experimental data in the optimal and overdoped regime. In the underdoped regime, we use the theory of electron-electron interaction in disordered conductors to explain the pseudo-gap behaviour.