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Strong electron-phonon interactions in cuprates and other high-temperaturesuperconductors have gathered support over the last decade in a large number ofexperiments. Here I briefly introduce the Froehlich-Coulomb multi-polaron modelof high-temperature superconductivity, which includes strong on-site repulsivecorrelations and the long-range Coulomb and electron-phonon (e-ph)interactions. Our extension of the BCS theory to the strong-coupling regimewith the long-range \emph{unscreened} electron-phonon interaction couldnaturally explain the isotope effects, unconventional thermomagnetic transport,and checkerboard modulations of the tunnelling density of states in cuprates.Comment: 11 pages, 4 figures, invited paper at the International Conference  'Stripes-04' (Rome, Italy, 26 Sept- 2 Oct, 2004), more Nernst data are  discusse

journal of superconductivity

High Temperature Superconductivity Due to a Long-Range Electron–Phonon Interaction, Application to Isotope Effects, Thermomagnetic Transport and Nanoscale Heterogeneity in Cuprates