in this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.

Differentials are an important topic in algebraic geometry, allowing the use of some classical geometric arguments in the context of varieties over any field. We will use them to define the genus of a curve, and to analyze the ramification of morphisms between curves. Although differentials remain important for arbitrary varieties, we will restrict our treatment to the case of nonsingular varie...

We’ve hit the big three theorems of vector calculus: Green’s, Stokes’, and the Divergence Theorem (although Green’s theorem is really a pretty obvious special case of Stokes’ theorem). But it’s an amazing fact that all of these theorems are really special cases of an even larger theorem that unifies all that we’ve studied so far. This new theory also extends what we’ve done to spaces of arbitra...