Motivic Spectral Invariants and Symplectic Microlocal Calculus of Pseudo-Differential Operators on Non-Archimedean Berkovich Spacetimes
Year: 2025
Type: article
Abstract: Mathematical Applications of Science Fiction We construct a rigorous framework for symplectic mi-crolocal calculus over non-Archimedean fields, specificallyfocusing on Berkovich analytic spaces. By introducinga category of motivic microlocal sheaves, we define anew class of spectral invariants associated with pseudo-differential operators acting on the rigid analytic étale site.We prove that the spectral distribution of the Frobeniusoperator on the crystalline realization of these sheavesconverges to the fixed-point Floer homology of the skele-ton of the Berkovich space. Furthermore, we establish acorrespondence between the motivic L-functions of theunderlying perfectoid space and the symplectic capac-ity of the Lagrangian submanifolds. This resolves theVoidwalker-Tate conjecture regarding the quantization ofnon-Archimedean phase spaces.
Authors: Revista, Zen, MFC, 10
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117704341
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