|Module title||Galois Cohomology, An Undergraduate Course|
|Module lecturer||prof. dr hab. Grzegorz Banaszak|
|Faculty||Faculty of Mathematics and Computer Science|
Module aim (aims)
Galois Cohomology is a one of the most important tools in Arithmetic Algebraic Geometry. The purpose of this course is a presentation of basic methods and results of Galois Cohomology. This course will also discuss results from other areas of Mathematics that are in the foundations of Galois Cohomology.
Pre-requisites in terms of knowledge, skills and social competences (where relevant)
Basic courses in Linear Algebra and Abstract Algebra.
Week 1: Field Theory
Week 2: Field theory
Week 3: Galois Theory
Week 4: Galois Theory
Week 5: Modules, complexes, cohomology.
Week 6: The group ring. Cohomology of groups.
Week 7: Cohomology of groups. Shapiro's lemma.
Week 8: Inflation, restriction and corestriction.
Week 9: Topological groups. Inverse systems.
Week 10: Profinite groups. Discrete G-modules.
Week 11: Galois Cohomology; basic properties
Week 12: Galois Cohomology
Week 13: Applications of Galois Cohomology
Week 14: Applications of Galois Cohomology
Week 15: Galois cohomology and Arithmetic Algebraic Geometr
- J.W.S. Cassels, A. Frochlich „Algebraic Number Theory” , Academic Press, (1967)
- J-P Serre, „Galois Cohomology”, Springer 1997
- S. Shatz, „Profinite Groups, Arithmetic and Geometry”, Annals of Math. Studies, Princeton Univ. Press 1972
- L. Washington, „Galois Cohomology”, article in the book „Modular forms and Fermat's last theorem”, Springer 1997