Differential fppf descent obstructions

In this dissertation, we consider the category of schemes equipped with a derivation and investigate a differential analogue of the fppf site on a differential scheme. We interpret the obstruction to the existence of integral points in affine varieties given by certain differential equations introduced by Voloch as the descent obstruction associated with torsors under a certain sheaf for our differential fppf topology. We also consider a multiplicative analogue of those differential descent obstructions and show that it is the only obstruction to the existence of integral points in affine varieties over function fields. Finally, we describe the obstruction set in the case of smooth projective isotrivial curves of genus g > 1 over a function field, extending a result of Voloch.