Let $X$ be a 'nice' topological space. Let $\left(U_i\right)_{i\in I}$ be a finite open covering of $X$. Let $\mathcal{F}$ be a sheaf of abelian groups.

For a subset $A\subset I$ denote $$U_A:=\cap_{i\in A}U_i.$$

Does there exist a spectral sequence which converges to the cohomology $H^*(X,\mathcal{F})$ and which starts at $$\bigoplus_{|A|=p}H^q(U_A,\mathcal{F}_{U_A})?$$

Here $\mathcal{F}_{U_A}$ denotes the restriction of $\mathcal{F}$ to $U_A$.

A reference will be helpful.