Fiches de cours 2017-2018

PDF
 

Sheaf cohomology

MATH-693

Lecturer(s) :

Patakfalvi Zsolt
Pieropan Marta
Zdanowicz Maciej Emilian

Language:

English

Remarque

Next time: Spring 2018

Summary

This is a course on the third chapter of the book “Hartshorne: Algebraic geometry” treating the foundations of the coho-mology theory of sheaves.

Content

This is a course on the third chapter of the book 'Hartshorne: algebraic geometry' treating the foundations of the cohomology theory of sheaves. The special feature of algebraic geometry is that students have to learn it twice. First, using the 'traditional' or 'classical' point of view, and then using the more general theory of schemes. So, this is a course for those ho have already learned the former and want to learn now the latter, and furthermore they already took the previous part of this series of courses, called 'Scheme theory'.

'Hartshorne: Algebraic Geometry' is the standard foundational graduate textbook for scheme theory. It is famous about the particular approach that the big chunk of the material is in the exercises.

The goal is to read the material at home, and present all the exercises during the meetings. Each student presents one or more exercises per week. This is a course only for those who have taken a course which is at least equivalent to the alge-braic geometry masters course here at EPFL.

Warning: the course is hard, as the book and the subject is famously hard. Significant work is needed to be put in at home.

Keywords

algebraic geometry, cohomology theory of sheaves

Learning Prerequisites

Required courses

Algebraic geometry (masters course), Scheme theory (PhD course)

Learning Outcomes

By the end of the course, the student must be able to:

Resources

Bibliography

Hartshorne: Algebraic Geometry

In the programs

  • Mathematics (edoc), 2017-2018
    • Semester
    • Exam form
      Oral
    • Credits
      4
    • Subject examined
      Sheaf cohomology
    • Lecture
      14 Hour(s)
    • Exercises
      28 Hour(s)
    • Practical work
      14 Hour(s)

Reference week

Lecture
Exercise, TP
Project, other

legend

  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German