\begin{tikzcd}
H^i(k,G) \arrow[r] \arrow[dr, "F^n"'] & H^i(k^{p^{-n}}, G) \arrow[d, "\wr"] \\
 & H^i(k, G^{(p^n)})
\end{tikzcd}

\begin{tikzcd}
G \arrow[d, "p"'] & G^{(p^n)} \arrow[l, "p^n"'] \arrow[d] & G \arrow[l, "F^n"'] \arrow[dl, "p"] \\
S & S \arrow[l, "\varphi_S"] &
\end{tikzcd}

\begin{tikzcd}
e \arrow[r] & K \arrow[r] \arrow[d] & G \arrow[r, "d"] \arrow[d, "u"] & G/K \arrow[r] \arrow[d, "v"] & e \\
e \arrow[r] & K/K \cap I \arrow[r] & G/I \arrow[r, "d'"] & G/KI \arrow[r] & e
\end{tikzcd}

\begin{tikzcd}
H^1(k,I) \arrow[r] \arrow[d] & H^1(k, I/I \cap K) \arrow[d] \\
H^1(k,G) \arrow[r, "d_1"] \arrow[d, "u_1"'] & H^1(k, G/K) \arrow[d, "v_1"] \\
H^1(k, G/I) \arrow[r, "d_1'"] & H^1(k, G/KI)
\end{tikzcd}

\begin{tikzcd}
C \arrow[r] \arrow[d] & C_B \arrow[d] \\
\widehat{C} = \mathrm{Hom}_A(\mathcal{U}, A) \arrow[r] &
\widehat{C}_B = \mathrm{Hom}_B(\mathcal{U}_B, B)
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small, nodes={font=\scriptsize}]
\text{Spéc Bil typ.} \arrow[r] \arrow[d] & \text{Bil typ} \arrow[d] & \text{Quad unim.} \arrow[dl] \arrow[d] & \text{Alt} \arrow[ddd] & \text{Spéc Alt} \arrow[l] \arrow[ddd] \\
\text{Spéc Bil unim.} & \text{Bil unim.} \arrow[d] & \text{Quad typ.} \arrow[d] & & \\
 & \text{Bil} \arrow[r, bend left=15] & \text{Quad} \arrow[l, bend left=15] & & \\
 & & \text{Mod} & \text{Mod unim.} \arrow[l] & \text{Spéc Mod unim.} \arrow[l]
\end{tikzcd}

\begin{tikzcd}
e \arrow[r] & \mu_2 \arrow[r] & \mathrm{Pin}(m) \arrow[r] & O(m) \arrow[r] & e \\
e \arrow[r] & \mu_2 \arrow[r] \arrow[u, no head, "\Vert" description] & \mathrm{Spin}(m) \arrow[r] \arrow[u] & SO(m) \arrow[r] \arrow[u, hook] & e
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
0 \arrow[r] & E'(A) \arrow[r] \arrow[d, "2"] & E(A) \arrow[r] \arrow[d, no head] & E(K) \arrow[r] \arrow[d, no head] & 0 \\
0 \arrow[r] & \sum E'(\hat A_p) \arrow[r] & \sum E(\hat A_p) \arrow[r] & \sum E(K_p) \arrow[r] & 0
\end{tikzcd}

\begin{tikzcd}[column sep=small, row sep=small]
0 \arrow[r] & F'(A) \arrow[r] & F(A) \arrow[r] \arrow[d] & F(K) \arrow[d] & \\
 & 0 \arrow[r] & \sum F(\hat A_p) \arrow[r, "\text{inj}"'] & \sum F(K_p) &
\end{tikzcd}