In the last years ample experimental evidence has shown that charge carriers in high-temperature superconductors are strongly correlated but also coupled with lattice vibrations (phonons), signaling that the true origin of high-Tc superconductivity can only be found in a proper combination of Coulomb and electron-phonon interactions. On this basis, we propose and study a model for high-Tc superconductivity, which accounts for realistic Coulomb repulsion, strong electron-phonon (Frohlich) interaction and residual on-site (Hubbard tilde{U}) correlations without any ad-hoc assumptions on their relative strength and interaction range. In the framework of this model, which exhibits a phase transition to a superconducting state with a critical temperature Tc well in excess of 100K, we emphasize the role of tilde{U} as the driving parameter for a BEC/BCS crossover. Our model lays a microscopic foundation for the polaron-bipolaron theory of superconductivity. We argue that the high-Tc phenomenon originates in competing Coulomb and Frohlich interactions beyond the conventional BCS description.
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