Fiches de cours 2018-2019

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Positive characteristic algebraic geometry

MATH-697

Lecturer(s) :

Patakfalvi Zsolt

Language:

English

Remarque

Next time: Fall 2018

Summary

This is a course on the geometry of algebraic varieties defined over fields of positive characteristic.

Content

The goal of the course is to learn the most possible techniques in positive characteristic algebraic geometry geometry. Examples of such techniques are: techniques connected to Kodaira vanishing and non-vanishing, such as torsor- and semi-positivity-method, bend and break, Keel's lifting statement, Forbenius trace method, generic vanishing in positive characteristic. Students will learn as much of these techniques as possible during a semester.

The required background for the course is a decent foundation of algebraic geometry, that is, a knowledge of Hartshorne's graduate textbook 'Algebraic Geometry'.

 

 

Keywords

algebraic geometry, positive characteristic

Learning Prerequisites

Required courses

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

Learning Outcomes

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

Resources

Notes/Handbook

  provided course notes 

In the programs

    • Semester
    • Exam form
       Oral presentation
    • Credits
      3
    • Subject examined
      Positive characteristic algebraic geometry
    • Lecture
      28 Hour(s)
    • Exercises
      14 Hour(s)

Reference week

 
      Lecture
      Exercise, TP
      Project, other

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