Differentials on the arc space after de Fernex and Docampo

We will present the main results  in [dFD] and the ideas behind them. In particular, given an arbitrary scheme $X$ over a base scheme $S$ we will explain how to describe the sheaf of relative differentials (with respect to $S$) of its arc and jets spaces (respectively $\Omega_{(X/S)_{\infty}/S}$ and $\Omega_{(X/S)_n/S}$) from the sheaf of relative differentials of $X$ ($\Omega_{X/S}$), and how to deduce an interesting decomposition of the fiber of $\Omega_{(X/S)_n/S}$ over a jet.

[dFD] De Fernex, T. and Docampo, R. Differentials on the arc space. https://arxiv.org/pdf/1703.07505.pdf, preprint 2017.