Student CA Seminar - Kähler Differentials and Generic Smoothness

Abstract: A derivation is a function that generalizes certain aspects of the derivative operator in an algebraic setting. In this talk, we first construct the module of Kähler differentials, which is the algebraic analog of the cotangent bundle on a manifold. Following this, we prove two exact sequences that assist in explicit computations of this module. Finally, we show that for a variety, the set of smooth points is open and dense.