Algebraic Number Theory II
Uwe Jannsen
Exercise sheet 4
Exercise 1 Let G be a (topological) group, let N ≤ G be a normal subgroup, and let A be a (continuous) G-module. Show that the sequence
0 //H1(G/N, A) Inf //H1(G, A) Res //H1(N, A) is exact.
Exercise 2 LetL/K be a Galois extension with Galois group G. Show that (a) H0(G, L) = K.
(b) Hn(G, L) = 0 for n >0.
