Which are the mechanisms of the correlation between atmospheric carbon dioxid and global warming/cooling?
Except from the obvious that carbon dioxide is more soluble in cold water and perhaps that some carbon dioxide is trapped in glacial ices, which are the known mechanisms?


Those obvious mechanisms, particularly the first, are the primary mechanisms. Atmosphere carbon dioxide content gradually drops to very low levels during a glaciation precisely because cold water can dissolve much more carbon dioxide than can warm water.

When the Milankovitch cycles reaches a stage where the Earth starts warming up at the end of a glaciation, the Earth's waters start warming up, too. The warmer waters cannot hold as much CO2 as they held during the glaciation. The CO2 comes out of solution, adding to the Milankovitch-driven warming. This is one of the key reasons why the exit from a glaciation is much more abrupt than is the entry into one.



Based on comments by the OP, the OP appears to doubt that carbon dioxide and other polyatomic gases are greenhouse gases. The three principal components of the dry atmosphere, nitrogen (N2), oxygen (O2), and argon, are not greenhouse gases. Electronically neutral monatomic gases and diatomic gases comprising two atoms the same substance have zero dipole moment. These gases have essential zero cross section to low energy (e.g., thermal infrared) photons.

On the other hand, polyatomic molecules have many more degrees of freedom than do the homogeneous diatomic molecules and monoatomic gases that comprise the bulk of our atmosphere. Some such as water vapor have a marked permanent dipole moment. Others such as carbon dioxide nominally have a zero dipole moment, but transients due to thermal vibrations can temporarily given them a non-zero dipole moment. The combination of increased degrees of freedom and a non-zero dipole moment make these polyatomic gases very good at absorbing some parts of the thermal infrared spectrum.

All other things being equal, adding greenhouse gases to the Earth's atmosphere increases the Earth's equilibrium temperature. It's important to note that this greenhouse effect is essential for life. Without it, the Earth would be a frozen icefall, from pole to pole. In fact, during the Cryogenian (850-635 million years ago) the Earth apparently was covered or nearly covered with ice from pole to pole.

The end of a glaciation adds significant portions of the two most important greenhouse gases to the Earth's atmosphere. Water vapor increases because a warmer atmosphere can hold more water vapor than can a cold one. Carbon dioxide increases because a warmer ocean can hold less carbon dioxide than can a cold one.

While the OP asked about the end of a glaciation, the real question being asked was about what is happening now. What happened at the end of glaciations and what is happening now are one and the same thing. Adding greenhouse gases to the Earth's atmosphere increases the Earth's equilibrium temperature. The end of a glaciation added greenhouse gases to the Earth's atmosphere, making the subsequent warming very rapid. Humanity is adding greenhouse gases to the atmosphere, carbon dioxide in particular, resulting in an even more rapid warming than that that occurred at the end of a glaciation.