Geometry of Schemes (first part)
A.Y. 2018/2019
Learning objectives
The course provide an introduction to the general theory of schemes and their main properties.
Expected learning outcomes
The students will acquire some basic expertees that should allow them to approach some research subjects, such as the geometry of moduli spaces.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
The course aims at giving an introduction to the theory of schemes. A scheme is a vast algebraic generalization of the concept of topological variety and allows to deal with objects which are apparently very different. For example, the affine line over the complex numbers or (the spectrum) of the ring of integers Z are very similar from the point of view of schemes. We will introduce the notion of scheme, of sheaf on a scheme and of morphism of schemes with plenty of examples. We will then study the cohomology of a sheaf on a scheme and its main properties.
We will try to be as much as possible selfcontained. In particular, we will recall the besic definitions and results from commutative algebra which are needed.
We will try to be as much as possible selfcontained. In particular, we will recall the besic definitions and results from commutative algebra which are needed.
Professor(s)
Reception:
Fix an appointment by email
Dipartimento di Matematica "F. Enriques" - Room 2046