  The finite-temperature phase diagram of the attractive Hubbard model is
studied by means of the Dynamical Mean Field Theory. We first consider the
normal phase of the model by explicitly frustrating the superconducting
ordering. In this case we obtain a first-order pairing transition between a
metallic phase and a paired phase formed by strongly coupled incoherent pairs.
The transition line ends in a finite temperature critical point, but a
crossover between two qualitatively different solutions still occurs at higher
temperature. Comparing the superconducting and the normal phase solutions, we
find that the superconducting instability always occurs before the pairing
transition in the normal phase takes place, i.e., $T_c > T_{pairing}$.
Nevertheless, the high-temperature phase diagram at $T > T_c$ is still
characterized by a crossover from a metallic phase to a preformed pair phase.
We characterize this crossover by computing different observables that can be
used to identify the pseudogap region, like the spin susceptibility, the
specific heat and the single-particle spectral function.

Superconductivity;Strongly Correlated Electrons