Hi.
Has some one an example of sheaf $A$ on flat morphism $f:X\rightarrow S$ of reduced complex spaces with fibers of constant positive dimension (or locally noetherian excellent schemes without embedded components) which satisfies the properties :
1) there is a dense open subset $V$ of $X$ (smooth or Cohen-Macaulay locus) on which $A$ is canonically null,
2) For every subset $F$ s.t $F\cap f^{-1}(s)$ has empty interior in $f^{-1}(s)$, we have ${\cal H}^{0}_{F}(A) = 0$,
3) There is some fibers on which the restriction of $A$ is not trivialy null.
Thank you.