Cohomological characterization of vector bundles

In my talk, I will address the problem of giving a cohomological characterization of vector bundles on algebraic varieties. This is a longstanding problem in Algebraic Geometry which has its roots in an old paper by Horrocks where he gave a cohomological characterization of line bundles on projective spaces $\mathbb P^n$.
In my talk, I will give a cohomological characterization of the bundle of $p$-differential forms on multiprojective spaces $\mathbb P^{n_1}\times\dots\times\mathbb P^{n_s}$ and a cohomological characterization of Steiner bundles on algebraic varieties. As a main tool I will use a generalized version of Beilinson's spectral sequence.
This is joint work with Costa and Soares.