Almost equivalences between Tamarkin category and Novikov sheaves

We revisit the relationship between the Tamarkin’s extra variable $t$ and Novikov rings. We prove that the equivariant version of Tamarkin category is almost equivalent (in the sense of almost mathematics) to the category of derived complete modules over the Novikov ring.

💡 Research Summary

The paper revisits the long‑standing relationship between Tamarkin’s extra variable t—originally introduced in microlocal sheaf theory to encode “time” or “action” in sheaf quantization—and the Novikov ring, which appears in Floer theory as a bookkeeping device for symplectic area. While previous works have identified t with the Laplace dual of ℏ⁻¹ in WKB analysis and with the exponential valuation of the universal Novikov variable, a precise categorical link between the equivariant Tamarkin category and the derived‑complete modules over the Novikov ring has been missing.

The author’s main result (Theorem 1.1) establishes an “almost embedding”
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