Abstract：

In the BV formalism the spaces of fields are presented as complexes whose cohomology returns the physical content. Different but equivalent complexes may be used, which turns out to be important conceptually and in practice. One useful operation is that of a partial integration (BV pushforward), which produces a chain map that, under some assumptions, is a quasiisomorphism. This has several applications: construction of observables (often as L_\infty representations), renormalization à la Wilson, highly nontrivial equivalences of theories. I will discuss some examples.