Mrinal Kanti Das

The following theorem, due to Horrocks (1964), is a monic inversion theorem : Let $A$ be a local ring and $P$ be a finitely generated projective $A[X]$-module. If $P_{f}$ is free for some monic polynomial $f\in A[X]$, then $P$ is free. The aim of this talk is to discuss similar monic inversion theorems and their impact on the development of the theory of projective modules over polynomial algebras. We will report on some recent results and discuss a few questions.