Lekili–Ueda's conjecture for complements of smooth ample divisors

Let VV be a compact Calabi–Yau manifold, and let ZVZ\subset V be a smooth ample divisor. Set U=VZU=V\setminus Z, which is a Weinstein manifold. Let Fukw(U)\mathrm{Fuk}^{w}(U) be the graded wrapped Fukaya category and let Fukc(U)\mathrm{Fuk}^{c}(U) be the subcategory generated by objects supported on compact Lagrangians. Lekili–Ueda's conjecture. There is an equivalence

Fukw(U)/Fukc(U)Fuk(Z).\mathrm{Fuk}^{w}(U)/\mathrm{Fuk}^{c}(U)\simeq \mathrm{Fuk}(Z).

This predicts that the Fukaya category of the ample divisor is recovered from the wrapped category of its complement after quotienting compactly supported objects; it is presented as a conjectural relation to the work of Lekili and Ueda.

Sources & referencesView supporting material

Primary source

James Pascaleff and Nicolò Sibilla, “Singularity categories of normal crossings surfaces, descent, and mirror symmetry”, arXiv:2208.03896 (2022).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.