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Fix the direction of an arrow
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aisejohan committed Oct 8, 2015
1 parent 419c856 commit 6f67023
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Expand Up @@ -119,6 +119,7 @@ Jackson Morrow
Yusuf Mustopa
David Mykytyn
Josh Nichols-Barrer
Kien Nguyen
Thomas Nyberg
Masahiro Ohno
Catherine O'Neil
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10 changes: 7 additions & 3 deletions etale-cohomology.tex
Expand Up @@ -154,10 +154,14 @@ \section{The \'etale topology}
(resp.\ abelian group, vector space, etc) $\mathcal{F}(U)$,
\item for each pair $U, \ U'$ of \'etale schemes over $X$,
and each morphism $U \to U'$ over $X$ (which is
automatically \'etale) a restriction map $\rho^{U}_{U'}
: \mathcal{F}(U) \to \mathcal{F}(U')$
automatically \'etale) a restriction map
$\rho^{U'}_U : \mathcal{F}(U') \to \mathcal{F}(U)$
\end{enumerate}
These data have to satisfy the following {\it sheaf axiom}:
These data have to satisfy the condition that $\rho^U_U = \text{id}$
in case of the identity morphism $U \to U$
and that $\rho^{U'}_U \circ \rho^{U''}_{U'} = \rho^{U''}_U$
when we have morphisms $U \to U' \to U''$ of schemes \'etale over $X$
as well as the following {\it sheaf axiom}:
\begin{itemize}
\item[$(*)$] for every \'etale covering $\{ \varphi_i : U_i \to X\}_{i \in
I}$, the diagram
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