Although the BV complex was one of the motivating examples for derived algebraic geometry, it is not yet fully understood in this setting. On one side, Costello's interpretation of the BV complex as function algebra of a certain derived critical locus does not explain symmetries that do not close off-shell, and on the other side, there still does not exist a canonical way to treat the infinite dimensional space of fields. In the talk, will present certain research ideas motivated by the above problems.