Formality of derived intersections (Q462625)

Summary: We study derived intersections of smooth analytic cycles, and provide in some cases necessary and sufficient conditions for this intersection be formal. In particular, if \(X\) is a complex submanifold of a complex manifold \(Y\), we prove that \(X\) can be quantized if and only if the derived intersection of \(X^2\) and \(\Delta_Y\) is formal in \(\mathrm{D}^{\mathrm{b}}(X^2)\).