The modified Ruan crepant resolution conjecture with a flat gerbe

Let

be a semi-positive Gorenstein orbifold and let $Y$ be a crepant resolution. Let $U_1,,U_s$ be the nonexceptional quantum parameters, and let $,,$ be a basis of the relevant cohomology of $Y$. A class $=++$ is **exceptional** when it lies in the exceptional cohomology subspace. **Modified Ruan crepant resolution conjecture.** There are a flat gerbe

over $Y$ and elements

$$f_1,\ldots,f_r\in\mathbb{C}[\mathbb{U}_1,\ldots,U_s]$$

such that $f_i=0$ when $U_1=\cdots=U_s=0$, the class $f=f_1\varphi_1+\cdots+f_r\varphi_r$ is exceptional, and the Frobenius algebra of the small quantum cohomology of

$$is isomorphic to the Frobenius algebra obtained from the$$

-twisted small quantum cohomology of $Y$ by analytic continuation in $Q_{s+1},\ldots,Q_r$, if necessary, followed by

$$Q_i=\begin{cases}e^{f_i}U_i&1\leq i\leq s,\e^{f_i}&s<i\leq r.\end{cases}$$

This is the modified version of Ruan’s conjecture, incorporating a flat gerbe and a change of variables that allows the nonexceptional parameters to vary. The source states that it follows from the preceding conjectures, but the conjecture itself remains unproved here.