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
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: JP18K13405
Funding statement: This work was partially supported by World Premier International Research Center Initiative (WPI), MEXT, Japan and JSPS KAKENHI Grant Number JP18K13405.
Acknowledgements
I would like to thank Kohei Iwaki, Tsukasa Ishibashi, Hiroshi Ohta, and Vivek Shende for many comments and discussions. Especially, Iwaki-san asked me to find a relationship between exact WKB analysis and microlocal sheaf theory for some years. I am very happy to write this note as my “homework report” of his lectures. I also would like to thank the anonymous referees for many comments.
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Articles in the same Issue
- Frontmatter
- Inverse mean curvature flow and Ricci-pinched three-manifolds
- Irregular loci in the Emerton–Gee stack for GL2
- Stationary measures for SL2(ℝ)-actions on homogeneous bundles over flag varieties
- The Lichnerowicz Laplacian on normal homogeneous spaces
- Sharp pinching theorems for complete submanifolds in the sphere
- On Vafa–Witten equations over Kähler manifolds
- Sheaf quantization from exact WKB analysis
- Reduced resonance schemes and Chen ranks
- Eisenstein degeneration of Euler systems
- Erratum to Discriminants and Artin conductors (J. reine angew. Math. 712 (2016), 107–121)
Articles in the same Issue
- Frontmatter
- Inverse mean curvature flow and Ricci-pinched three-manifolds
- Irregular loci in the Emerton–Gee stack for GL2
- Stationary measures for SL2(ℝ)-actions on homogeneous bundles over flag varieties
- The Lichnerowicz Laplacian on normal homogeneous spaces
- Sharp pinching theorems for complete submanifolds in the sphere
- On Vafa–Witten equations over Kähler manifolds
- Sheaf quantization from exact WKB analysis
- Reduced resonance schemes and Chen ranks
- Eisenstein degeneration of Euler systems
- Erratum to Discriminants and Artin conductors (J. reine angew. Math. 712 (2016), 107–121)