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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.


Spring 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)


  • Mon 11:05 - 11:55


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.


Bernhard Koeck
Phone 023 80 595125


Photo of Maxime Fairon
Maxime Fairon
Photo of Thomas Honey
Thomas Honey
Photo of James Macpherson
James Macpherson
(East Anglia)


Topologie algébrique et théorie des faisceauxGodement
Lectures on Riemann surfacesForster
Sheaf TheoryB.R. Tennison


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The assessment for this course will be via a single take-home paper with 2 weeks to complete and submit online. You will need 50% to pass.

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