Mathematics > Symplectic Geometry
[Submitted on 26 Jun 2020 (v1), last revised 4 Jul 2023 (this version, v5)]
Title:Sheaf quantization from exact WKB analysis
View PDFAbstract:A sheaf quantization is a sheaf associated to a Lagrangian brane. By using the ideas of exact WKB analysis, spectral networks, and scattering diagrams, 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 $\hbar$-enhanced Riemann-Hilbert correspondence.
Submission history
From: Tatsuki Kuwagaki [view email][v1] Fri, 26 Jun 2020 09:11:20 UTC (1,776 KB)
[v2] Mon, 12 Oct 2020 10:49:00 UTC (1,783 KB)
[v3] Tue, 22 Feb 2022 10:27:28 UTC (1,781 KB)
[v4] Mon, 17 Oct 2022 09:52:19 UTC (236 KB)
[v5] Tue, 4 Jul 2023 08:00:21 UTC (383 KB)
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