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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24347 |
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Table of Contents:
- We study the period map from infinitesimal deformations of a scheme $X$ over a perfect field $k$ to those of the associated $k$-linear $\infty$-category $\mathrm{QC}(X)$. For quasicompact, smooth, and separated $X$, we identify the corresponding map on tangent fibres with the dual HKR map $\mathrm{R}Γ(X, \mathrm{T}_X)[1] \to \mathrm{HH}^{\bullet}(X/k)[2]$, and give conditions for injectivity on homotopy groups. As applications, we prove liftability along square-zero extensions to be a derived invariant (at least when $\mathrm{char}(k) \ne 2$), and exhibit cases where the entire (classical) deformation functor of $X$ is a derived invariant; this partially answers a question of Lieblich.