MAGIC053: Sheaf Cohomology

Course details

Semester

Spring 2018
Monday, January 22nd to Friday, March 16th; Monday, April 23rd to Friday, May 4th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Mondays
11:05 - 11:55

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.

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

  • BK

    Dr Bernhard Koeck

    University
    University of Southampton

Bibliography

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Assessment

The assessment for this course will be released on Monday 7th May 2018 and is due in by Sunday 20th May 2018 at 23:59.

The assessment for this course will be via a single take-home paper with 2 weeks to complete and submit online. You will need at least 50 per cent to pass. The exam period is 7 May - 20 May, 2018.

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

Files

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Lectures

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