Research Projects

In affine algebraic geometry, one of the important classes of objects are algebraic structures which are not as nice as polynomial algebras, but they become polynomial algebras after a base change. In this project, we aim to study a type of such algebraic structure. To be specific, for any commutative ring $R$ we propose to study the $R$-algebras $A$ such that there exists a finite algebraic ring extension $S$ of $R$ satisfying $A \otimes_R S = S[X]$, i.e., polynomial algebra in one indeterminate over $S$; and correspondingly aim to answer a few questions related to Epimorphism problem.