MAGIC053: Sheaf Cohomology

Course details

A specialist MAGIC course


Autumn 2021
Monday, October 4th to Friday, December 10th


Live lecture hours
Recorded lecture hours
Total advised study hours


10:05 - 10:55


Sheaves and their cohomology play a fundamental role in modern Algebraic, Arithmetic and Differential Geometry. The goal of this course is to give a thorough introduction to the basics of sheaf cohomology and to give a panorama of sheaf theoretic applications. Elementary sheaf theory hardly needs any prerequisites other than general mathematical language, the cohomology of sheaves will be introduced only after the main result of homological algebra has been recalled, and background in the respective area would be useful for the final applications.


See Course Description.


  • Elementary sheaf theory;
  • Cohomology of abelian sheaves;
  • Injective, flabby, acyclic, soft and fine sheaves;
  • Brief survey on sheaf cohomology for topological and differentiable manifolds, for Riemann surfaces and for algebraic varieties.


  • BK

    Dr Bernhard Koeck

    University of Southampton


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The assessment for this course will be released on Monday 10th January 2022 and is due in by Sunday 23rd January 2022 at 23:59.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.


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