A Theorem of Cowsik and Nori

Abstract

This thesis is an expository account of a proof of the theorem of R.C.Cowsik and M.V. Nori (1978), which asserts that every algebraic curve in an affine space over a field of positive characteristic is a set theoretic complete intersection. In order to put this theorem in context, some background material is developed. At the end of the first chapter, the statement of the Cowsik-Nori theorem is precised. The proof of this theorem that is presented in this thesis, depends crucially on a theorem of Ferrand - Szpiro and Mohan Kumar. The final and third chapter of this thesis presents a proof of the Cowsik-Nori theorem. Concluding remarks related to the main theme of this thesis are given in the end of the third chapter.