  BRST complexes are differential graded Poisson algebras. They are associated
to a coisotropic ideal $J$ of a Poisson algebra $P$ and provide a description
of the Poisson algebra $(P/J)^J$ as their cohomology in degree zero. Using the
notion of stable equivalence introduced by Felder and Kazhdan, we prove that
any two BRST complexes associated to the same coisotropic ideal are
quasi-isomorphic in the case $P = \mathbb{R}[V]$ where $V$ is a
finite-dimensional symplectic vector space and the bracket on $P$ is induced by
the symplectic structure on $V$. As a corollary, the cohomology of the BRST
complexes is canonically associated to the coisotropic ideal $J$ in the
symplectic case. We do not require any regularity assumptions on the
constraints generating the ideal $J$. We finally quantize the BRST complex
rigorously in the presence of infinitely many ghost variables and discuss
uniqueness of the quantization procedure.
