Batalin–Vilkovisky semi-infinite pairing conjecture

Let $n$ be the dimension parameter specified in the source, and let $BV^i(N,N')$ denote the cohomology of the total Koszul bicomplex associated with the finite-dimensional approximation indexed by $N,N'$. Write $BV^{i+\frac{\infty}{2},w}$ for the corresponding weight-space limit. Batalin–Vilkovisky pairing conjecture. One can define

$$BV^{i+\frac{\infty}{2}}=\bigoplus_w BV^{i+\frac{\infty}{2},w},\qquad BV^{i+\frac{\infty}{2},w}=\underset{N\to\infty}{\lim}\,\underset{N'\to\infty}{\lim}\,BV^{i+\operatorname{codim}\mathpzc{Z}(0,N')+Nn}(N,N')^w,$$

and there is a nondegenerate pairing

$$BV^{i+\frac{\infty}{2}}\otimes BV^{k-i+\frac{\infty}{2}}\to\mathbb{C},$$

where $k$ is the integer from the preceding conjecture. This proposes a BV-type semi-infinite cohomology theory with a duality pairing analogous to the local-cohomology construction.