Sheaf quantization from exact WKB analysis
arXiv:2006.14872
Abstract
A sheaf quantization is a sheaf associated to a Lagrangian brane. By using the results of exact WKB analysis, we sheaf-quantize spectral curves over the Novikov ring under some assumptions on the behavior of Stokes curves. For Schrödinger equations, we prove that the local system associated to the sheaf quantization (microlocalization a.k.a. abelianization) over the spectral curve can be identified with the Voros--Iwaki--Nakanishi coordinate. We expect that these sheaf quantizations are the object-level realizations of the -enhanced Riemann--Hilbert correspondence.
v6: 42 pages. Final version to appear in Crelle's journal. Section 10 has been removed, and an expanded version will appear as a separate paper