2025/03/20 by Tatsuki Kuwagaki, Kuwagaki, Tatsuki, Baiyun Zhang +1 · 2 citations
Computer Science · Mathematics · Decision Sciences · #Advanced Algebra and Logic #Rings, Modules, and Algebras #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2503.15933
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.