J-M Schemes And Morphisms

In this thesis, we mainly investigate J-M schemes and morphisms of J-M schemes.We divide the thesis in four chapters.The first chapter is introduction, in this chapter, we have attempted to outline the motivation of advancing the definition of J-M scheme.In the second chapter, first and foremost, the definition of J-M scheme is given. Then we study some properties about J-M schemes satisfying some additional conditions, such as integral J-M scheme, reduced J-M scheme, and locally noetherian J-M scheme. Moreover we obtain a number of properties about morphisms of J-M schemes. Finally, a criterion for affineness is obtained.In the third chapter, a series of definitions of morphisms satisfying some finite conditions are given, such as affine morphism of J-M schemes, locally of finite type morphism of J-M schemes and finite type morphism of J-M schemes. Then we study the properties about these morphisms.In the last chapter, we deals with the closed immersion of J-M schemes. Firstly the definition of closed immersion of J-M schemes is given. Then we obtain a charactarization of closed immersion.