Seminar on Galois Cohomology

University of Sheffield, Fall 2022

This seminar aims to study the foundations of the theory of Galois cohomology.

A short note on the seminar can be found HERE.

Talks will be on Fridays at 10am in J11 (not necessarily every week though).

TALKS:

  1. Profinite Groups (Serre I.1) (Gui, Sec. 3) (speaker: Jason)

  2. Cohomology of Profinite Groups (Serre I.2) (Gui, Sec. 10) (Har, I.4) (speaker: Constantinos)

  3. Cohomological Dimension (Serre I.3) (Har, I.5) (speaker: Andrew)

  4. The case of pro-p groups (and the Golod-Shafarevich inequality) (Serre I.4) (Har, I.3) (speaker: James B.)

  5. Galois cohomology: first examples and cohomological dimension criteria (Serre II.1 and II.2) (Har, I.6) (speaker: Ananyo)

  6. Fields of dimension at most one (Serre II.3) (speaker: Johannes)

  7. Transition theorems (Serre II.4)

  8. The case of p-adic fields (Serre II.5) (Har, II)

  9. The case of number fields (Serre II.6) (Har, III)


Bibliography:

[Ser] J.-P. Serre. Galois cohomology. Springer, Berlin, 1997 and 2002.

[Har] D. Harari. Galois cohomology and class field theory. Springer, Cham, 2020.


Additional sources:

P. Guillot. A gentle course in local class field theory. Local number fields, Brauer groups, Galois cohomology. Cambridge University Press, Cambridge, 2018.

J. Neukirch, A. Schmidt, K. Wingberg. Cohomology of number fields. Springer, Berlin, 2000 und 2008.

R. Sharifi. Group and Galois Cohomology (introductory level)