The paper by V. J. Emery discusses the high-$T_c$ superconductivity in oxide materials, specifically focusing on the mechanism of pairing. The author proposes that the charge carriers are holes in the O(2p) states, and the pairing is mediated by strong coupling to local spin configurations on the Cu sites. This model is consistent with the observed high transition temperatures in materials like YBa$_2$Cu$_3$O$_{6-\delta}$. The analysis is based on the quasi-two-dimensional motion of electrons within CuO$_2$ planes and an extended Hubbard model. The Hamiltonian includes hopping integrals and interaction terms, with parameters such as $t=1.3-1.5$ eV, $\epsilon \equiv \epsilon_{p}-\epsilon_{d}=1$ eV, $U_{p}=2-3$ eV, $U_{d}=5-6$ eV, and $V=1-2$ eV. The model predicts a gap $\Delta$ between occupied and unoccupied states, and the pairing is driven by the strong O(2p)-Cu(3d) exchange interactions. The BCS transition temperature is derived from the condition for a nontrivial solution of the gap equation, and the model can explain transition temperatures between 30 and 40 K. The paper also discusses the role of oxygen defects and the possibility of s-wave pairing in some materials.The paper by V. J. Emery discusses the high-$T_c$ superconductivity in oxide materials, specifically focusing on the mechanism of pairing. The author proposes that the charge carriers are holes in the O(2p) states, and the pairing is mediated by strong coupling to local spin configurations on the Cu sites. This model is consistent with the observed high transition temperatures in materials like YBa$_2$Cu$_3$O$_{6-\delta}$. The analysis is based on the quasi-two-dimensional motion of electrons within CuO$_2$ planes and an extended Hubbard model. The Hamiltonian includes hopping integrals and interaction terms, with parameters such as $t=1.3-1.5$ eV, $\epsilon \equiv \epsilon_{p}-\epsilon_{d}=1$ eV, $U_{p}=2-3$ eV, $U_{d}=5-6$ eV, and $V=1-2$ eV. The model predicts a gap $\Delta$ between occupied and unoccupied states, and the pairing is driven by the strong O(2p)-Cu(3d) exchange interactions. The BCS transition temperature is derived from the condition for a nontrivial solution of the gap equation, and the model can explain transition temperatures between 30 and 40 K. The paper also discusses the role of oxygen defects and the possibility of s-wave pairing in some materials.