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arXiv · 2503.15933

Almost mathematics, Persistence module, and Tamarkin category

Tatsuki Kuwagaki·Bingyu Zhang
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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.

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Tatsuki Kuwagaki, Bingyu Zhang. 2025-03-20. Almost mathematics, Persistence module, and Tamarkin category. https://arxiv.org/abs/2503.15933

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