Galois Cohomology

Summer semester 2021

We will study the cohomology of profinite groups, and some of its applications to Galois theory (in particular freeness or almost-freeness results for Galois groups of various specific fields). I will roughly follow Koch's book (see the literature section below).

Interested students should register by sending me an email.

Time and place

The course will be held online (at least for now), with lectures held Fridays 12.00-14.00 (starting Apr 16) on zoom. I will send a meeting invitation to registered students.

Notes

• lecture 1 (introduction)
• lecture 2 (profinite groups)
• lecture 3 (infinite Galois theory)
• lecture 4 (cohomology I)
• lecture 5 (cohomology II)
• lecture 6 (free pro-p groups I)
• lecture 7 (free pro-p groups II)
• lecture 8 (relations)
• lecture 9 (some algebraic number theory)
• lecture 10 (some clas field theory)
• lecture 11 (maximal p-extensions)
• lecture 12 (Galois groups of local fields)
• lecture 13 (Galois groups of global fields)

Literature

Koch, Galoissche Theorie der p-Erweiterungen.
Serre, Galois Cohomology.