### Description

Let I be an ideal in a commutative (associative) algebra O. Starting

from a resolution of O/I as an O-module, we construct a Koszul-Tate

resolution for this quotient, i.e.\ a graded symmetric algebra over O

with a differential which provides simultaneously a resolution as an

O-module. This algebra resolution has the beautiful structure of a

forest of decorated trees and is related to an A-infinity algebra on the

original module resolution.
Considering O to be a Poisson algebra

and I a finitely generated Poisson subalgebra, we use the above

construction to obtain the corresponding BFV formulation. Its cohomology

at degree zero is proven to coincide with the reduced Poisson algebra

N(I)/I, where N(I) is the normaliser of I inside O, thus

generalising ordinary coisotropic reduction to the singular setting. As

an illustration we use the example where O consists of functions on

T^*(\R^3) and I is the ideal generated by angular momenta.

This is joint work with Aliaksandr Hancharuk and, in part, with Camille

Laurent-Gengoux.