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General


Description

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.

Semester

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

Timetable

  • Mon 11:05 - 11:55

Prerequisites

See Course Description.

Syllabus

  • 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.

Lecturer


Bernhard Koeck
Email B.Koeck@soton.ac.uk
Phone 023 80 595125


Students


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


Bibliography


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


Note:

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Assessment



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.

No assignments have been set for this course.

Files



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Recorded Lectures


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