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lines changed Original file line number Diff line number Diff line change @@ -923,10 +923,10 @@ \section{Stalks}
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x\in U, s\in \mathcal {F}(U)
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\} /\sim
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$$
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- with equivalence relation given by $ (U, s) \sim (U', s')$
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- if and only if $ s|_{U \cap U'} = s'|_{U \cap U'} $ . By abuse of
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- notation we will often denote $ (U, s) $ , $ s_x $ ,
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- or even $ s$ the corresponding element in $ \mathcal {F}_x$ .
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+ with equivalence relation given by $ (U, s) \sim (U', s')$ if and only if
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+ there exists an open $ U'' \subset U \cap U'$ with $ x \in U'' $ and
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+ $ s|_{U''} = s'|_{U''} $ . By abuse of notation we will often denote
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+ $ (U, s) $ , $ s_x $ , or even $ s$ the corresponding element in $ \mathcal {F}_x$ .
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Also we will say $ s = s'$ in $ \mathcal {F}_x$ for two local sections
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of $ \mathcal {F}$ defined in an open neighbourhood of $ x$ to denote that
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they have the same image in $ \mathcal {F}_x$ .
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