Timeline for Description of Shapiro lemma by cochain

8 events

when toggle format	what		by	license	comment
Jul 17, 2018 at 7:41	comment	added	Pierre		@Qixiao : you have to take a transversal for $H$ in $G$... again, the details are in NSW, Cohomology of Number Fields. By the way, the isomorphism the other way around is easy: Shapiro's isomorphism is the restriction from $G$ to $H$, followed by the map $N\to M$ which evaluates at 1 -- thinking of the induced module as $Hom_{\mathbb{Z}H}( \mathbb{Z} G, M)$.
Jul 15, 2018 at 20:35	review	Close votes
Jul 18, 2018 at 20:44
Jul 15, 2018 at 20:24	comment	added	Chris Gerig		See also the exercise in Chapter III.8 of Ken Brown's "Cohomology of Groups".
Jul 15, 2018 at 14:44	comment	added	user39380		@TKe Thanks for the reference, I’ll try to work out the details! One thing a bit confusing, if we are constructing the reverse map $H^i(H,M)\to H^i(G,N)$, then a cocycle $H^i\to M$ can associate a cocycle $H^i\to N$ by inclusion, but then how does it extends to a cocycle on $G^i$?
Jul 15, 2018 at 14:28	history	edited	Carlo Beenakker	CC BY-SA 4.0	Schapiro --> Shapiro
Jul 15, 2018 at 14:27	history	edited	user39380	CC BY-SA 4.0	edited title
Jul 15, 2018 at 13:49	comment	added	user19475		See Cohomology of Number Fields, (1.6.4).
Jul 15, 2018 at 13:22	history	asked	user39380	CC BY-SA 4.0