Proposition 14

Tag 00JQ, permanent. Cite it as [Bourbaki, Tag 00JQ].

Algebra, VIII, p. 322, § 16. Other Descriptions of the Brauer Group

The following diagram commutes:

Br(L $/K$ ) $^{\Phi_{L/K}}/$ / $H_2(G,L_*)$

$r_{K'/K}$ Res $^G_H$

Br(L $/K'$ ) $^{\Phi_{L/K'}}/$ / $H_2(H,L_*)$ .

This follows from Propositions 7 of VIII, p. 299 and 13 of VIII, p. 317.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Theorem 6, § 16

Cites

VIII, p. 299
VIII, p. 317