Year: 2025
Type: preprint
Abstract: We give a precise unification of three theories that are widely used by symplectic geometers: (Almost) modules over the Novikov ring, Persistence modules, and the Tamarkin category. Our method provides new input in this direction, especially in relation to Vaintrob's Novikov/log-perfectoid mirror symmetry for Novikov toric schemes. The results of this paper can also be treated as a study of persistent homology from a higher algebra point of view. As applications, we establish a version of homological mirror symmetry over the Novikov ring for toric varieties and propose a conjecture for homological mirror symmetry over the Novikov ring for log Calabi-Yau varieties.
Source: arXiv (Cornell University)
Authors: Kuwagaki, Tatsuki, Zhang, Bingyu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415288162
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