% wormux level % felix salfelder 2007 \documentclass[landscape]{article} \usepackage{amsmath, amssymb} \usepackage[isolatin]{inputenc} \usepackage{german} \usepackage[matrix,arrow,cmtip,curve]{xy} \usepackage[active]{srcltx} %%%%%%%%%%% \pagestyle{empty} \newcommand{\ox}{\otimes} \newcommand{\OA}{\operatorname{A_\star}} \newcommand{\OB}{\mathbb B \times \{ a,b \}} \newcommand{\OC}{\mathbb C} \newcommand{\OD}{\mathcal D_+} \renewcommand{\OE}{{\coprod_{p}\mathcal F_p}} \newcommand{\OF}{{\operatorname{coker} \varphi}} \newcommand{\OG}{{\operatorname{Gal}( \mathbb{C} / \overline{ \mathbb Q})}} \newcommand{\OH}{\operatorname{H}^1} \newcommand{\OI}{\mathcal I} \newcommand{\OJ}{{\operatorname{M}(n,\mathbb F_3)}} \newcommand{\OK}{\Bbbk} \newcommand{\OL}{\mathcal L^p(\mathbb R;\mathbb C)} \newcommand{\OLL}{\underset{\leftarrow}{\lim}{\Omega_k}} \newcommand{\OM}{{\mathcal M^\bot} } \newcommand{\ON}{{\mathbb N_0} } \newcommand{\OO}{\mathcal O} \newcommand{\OOO}{0} \newcommand{\OP}{{\mathbb P_{\mathbb R}^2}} \newcommand{\OQ}{{\mathbb Q_p}} \newcommand{\OR}{{\mathbb R/ \mathbb Z}} \newcommand{\OS}{\bigoplus V_\alpha} \newcommand{\OT}{{\mathbb C \ox_\mathbb Z M}} \newcommand{\OU}{{\operatorname{SU}(3)}} \newcommand{\OW}{\mathcal W} \newcommand{\OV}{\mathcal U \ox_{\mathfrak b} \mathbb C_\mu} \newcommand{\OX}{\mathfrak X(T)} \newcommand{\OY}{{\mathfrak{sl}_3}} \newcommand{\OZ}{{\operatorname V(x^3-y^2)}} \newcommand{\MA}{x \mapsto tx} \newcommand{\MB}{\frac{\operatorname d}{\operatorname dt}} \newcommand{\MC}{{\partial}} \newcommand{\MD}{\iota} \newcommand{\ME}{{\operatorname{ext}}} \newcommand{\MF}{{f^\bullet}} \newcommand{\MG}{{\gamma(n)}} \newcommand{\MI}{{\int_\Gamma}} \newcommand{\MJ}{{\cdot^j}} \newcommand{\MK}{{\kappa}} \newcommand{\ML}{{\ell}} \newcommand{\MM}{{\cdot m_\alpha}} \newcommand{\MN}{{\nabla}} \newcommand{\MT}{{\tau}} % \newcommand{\MX}{{\begin{matrix} 1 & u\\ 0 &-1\end{matrix}}} \newcommand{\MX}{{x \mapsto x^2}} \newcommand{\MZ}{\zeta} \begin{document} $\xymatrix{ A \ar[d]^\MC &\OB \ar@{.>}[r] \ar[d] &\OK \ar[d] &\OS \ar[d]^MD & E \ar[d] &\OK\ar[rd]\ar@{<<-}[d] & G \ar[r]^{P(c)}\ar[d] &\OR \ar[d]_a \\ \OQ\ar[r] \ar[d] &\OU \ar[d]^\MC &\OP \ar@/_/[d]^\MJ &\OA\ar@{<-}[r] \ar@/_/[l]^\MF &\OK \ar[dr] \ar@{<--}[d] & F \ar@{-->}[r] \ar[d] &\OY\ar[r] \ar@{<<--}[d] & D \ar[d] \\ \OF\ar[r]^\MA \ar@{<..}[d] &\OH \ar[r] \ar[dd] &\OL \ar[r] \ar@{-->}[d] & D \ar@{<-}[r]_\MD \ar[d] & E \ar@{-->}[r] \ar@/_/[u] &\OD\ar[r] \ar@{->>}[d] \ar@{}[dr]|\square & G \ar@/_/[r] \ar[d] &\ON \ar[d] \\ \OC\ar@/_/[rr] \ar[d] & &\OE \ar[rd] \ar@{<-}[d] &\OOO\ar@{^{(}->}[r] \ar[d] &\OO \ar@{->>}[r] \ar[d] &\OR\ar[r] \ar[d] &\OC \ar[d] &\OS \ar[d] \\ \OJ\ar[r]^\MI \ar[d] &\OS \ar[r] \ar@{^{(}->}[d] &\OQ \ar[r]^\gamma \ar[d] &\OI\ar@{<--}[r] \ar@/^/[d] & E \ar[d] \ar@/_/[u] &\OW\ar[r] \ar@{->>}[l] \ar[d] &\OH\ar[ru] \ar@{-->}[d] &\ON \ar[d] \\ \OI\ar[r] \ar@{-->}[d] &\OT \ar[ru] \ar[rd] &\OLL\ar[r] &\OD\ar@{-->}[r] \ar[d] &\OZ \ar[ru]\ar[d] &\OF\ar[rd] \ar@{<-}[d] &\OL\ar[r]^\MX \ar[d] &\OV \ar[d] \\ \OX\ar[r] \ar[d]^\varphi &\OP \ar@{->>}[d] &\OG \ar[r] \ar[d]^\varrho &\OW\ar[r]^{f_\sharp} \ar[d] &\OX \ar[d]^\MT &\OG\ar[r]^\MG &\OX\ar[r] \ar[d] &\OR \ar[d] \\ \OL\ar[r]^\MG &\OX \ar[r] \ar@/^/@{-->}[r]^\MN &\OC & D \ar@{.>}[r] \ar[lu]^\MK &\OF \ar[r] \ar[ru]^\MZ &\OH\ar[r] &\OI\ar[r] &\OW \\ }$ \end{document}