Complete intersection ideals and a question of Nori

Abstract

This is my PhD thesis from 2004 under Prof. S.M. Bhatwadekar. Here we answer a question of Nori and prove the following result. Let $A$ be a smooth affine domain of dimension $d$ over an infinite perfect field. Let $I$ be an ideal of $A[T]$ of height $n$ such that $2n \geq d+3$. Given surjections $\phi:(A[T]/I)^n \rightarrow I/I^2$ and $\rho :A^n \rightarrow I(0)$ such that $\phi(0)=\rho \otimes A/I(0)$, then there exist a surjection $\Phi :A[T]^n \rightarrow I$ such that $\Phi(0)=\rho$ and $\Phi \otimes A/I =\phi$. This is a joint work with S.M. Bhatwadekar.