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.
From: Bingyu Zhang [view email]
[v1]
Thu, 20 Mar 2025 08:17:34 UTC (76 KB)
[v2]
Mon, 28 Apr 2025 17:57:33 UTC (77 KB)
[v3]
Wed, 24 Jun 2026 05:25:05 UTC (78 KB)
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