A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY
Hampton, Earl F.
The purpose of this thesis is to define the basic objects of study in algebraic geometry, namely, schemes and quasicoherent sheaves over schemes. We start by discussing algebraic sets as common zeros of polynomials and prove Hilbert's Nullstellensatz to establish a correspondence between algebraic sets and ideals in a polynomial ring. We then discuss just enough category theory to define a sheaf as a contravariant functor and then introduce ringed spaces, the spectrum of a ring, and the definition of affine schemes. We then discuss sheaves of modules over schemes. We then define projective varieties as ringed spaces. We end by proving Hilbert's syzygy theorem that can be used to study the equations defining projective varieties.
Hampton, Earl F.. (January 2010). A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY (Master's Thesis, East Carolina University). Retrieved from the Scholarship. (http://hdl.handle.net/10342/2797.)
Hampton, Earl F.. A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY. Master's Thesis. East Carolina University, January 2010. The Scholarship. http://hdl.handle.net/10342/2797. September 17, 2019.
Hampton, Earl F., “A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY” (Master's Thesis., East Carolina University, January 2010).
Hampton, Earl F.. A PRIMER FOR THE FOUNDATIONS OF ALGEBRAIC GEOMETRY [Master's Thesis]. Greenville, NC: East Carolina University; January 2010.
East Carolina University