Mayer-Vietoris sequence for sheaf cohomology
= Mayer-Vietoris sequence for sheaf cohomology
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{wiki=Mayer–Vietoris_sequence#Other_forms}
For $X=U\cup V$, the short exact sequence of sheaves obtained by restricting to $U$, $V$, and $U\cap V$ induces a long exact sequence
$$
0\to H^0(X,\mathcal F)\to H^0(U,\mathcal F)\oplus H^0(V,\mathcal F)\to H^0(U\cap V,\mathcal F)\to H^1(X,\mathcal F)\to\cdots.
$$