= Punctured affine three-space
{title2=$\mathbb A_k^3\setminus\{0\}$}
For $U=\mathbb A_k^3\setminus\{0\}$,
$$
H^0(U,\mathcal O_U)=k[x_1,x_2,x_3],\qquad H^1(U,\mathcal O_U)=0,
$$
and
$$
H^2(U,\mathcal O_U)\cong
\frac{k[x_1^{\pm1},x_2^{\pm1},x_3^{\pm1}]}{
k[x_1^{\pm1},x_2^{\pm1},x_3]+k[x_1^{\pm1},x_2,x_3^{\pm1}]+k[x_1,x_2^{\pm1},x_3^{\pm1}]}.
$$
The last group has basis represented by $x_1^{-a}x_2^{-b}x_3^{-c}$ for $a,b,c\geq1$, and all groups in degrees at least three vanish.
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