Schemes - An introduction to modern algebraic geometry
Lecturer: Pedro Nuñez
Date: 22/03/2017
Time: 17:00
Place: Room 103
Abstract: Our goal in this talk will be to justify the introduction of schemes in algebraic geometry.
We will first give an overview of classical algebraic geometry over an algebraically closed field. After this, we will give a brief introduction to the theory of sheaves, keeping always in mind the example of the sheaf of regular functions on an algebraic variety. Then we will see how schemes arise as the natural way to generalize and extend our algebraic varieties. Finally we will discuss two key constructions with schemes, namely the gluing and the fibered product of schemes.
With all this machinery, we will be able to give a glimpse of the powerful generalizations achieved with the introduction of schemes in alge- braic geometry, such as the integration of algebraic number theory and algebraic geometry, leading for example to Deligne’s proof of the Weil Conjecture.
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Lecture notes
Bibliography
- Hartshorne, Algebraic Geometry
- David Eisenbud and Joe Harris, The geometry of schemes
- Vakil, Math 216: Foundations of algebraic geometry
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