Evolving plan for the coming lectures, Math 603, spring 2021

• 3/22/2021: cup products in group cohomologies and Tate cohomology groups, restriction-inflation sequence, cohomological triviality, toward Tate's theorem (for a "fundamental class")
• 3/15/2021: More about group cohomology and Galois cohomology, cohomology of cyclic groups, Tate cohomology
• 3/12/2021: Kummer theory, Artin-Schreier theory, Galois cohomology
• 3/08/2021: algebraic independence of character, normal basis theorem, Galois cohomology, Hilbert theorem 90
• 3/05/2021: algebraic independence of characters, normal basis theorem, generalities on Galois cohomology, Hilbert theorem 90
• 3/01/2021: linear independence of characters, norm and trace, Hilbert's theorem 90 for cyclic extensions, normal basis theorem
• 2/26/2021: the fundamental theorem of Galois theory (for finite Galois extensions, linear independence of characters (i.e. field embeddings), norm and trace, Hilbert's theorem 90 for cyclic extensions
• 2/22/2021: purely inseparable element, purely inseparable extensions, normal extensions, Galois extensions, derivations