An obstruction to lifting schemes to spectral schemes

Robert Szafarczyk

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arXiv · 2607.11853

An obstruction to lifting schemes to spectral schemes

Robert Szafarczyk

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Abstract

$\hat\delta$-rings are a globalization of $\delta$-rings. Motivated by their application to obstructing spectral lifts, we develop the theory of animated $\hat\delta$-rings. They extend the discrete notion in the same way that animated $\delta$-rings extend that of $\delta$-rings, but are not given by the process of animation. We also generalize the definition to schemes and extend the obstruction to this setting. We apply it to concrete examples such as number rings, closed subschemes of $\mathbb P^n$, and various group schemes.

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Robert Szafarczyk. 2026-07-13. An obstruction to lifting schemes to spectral schemes. https://arxiv.org/abs/2607.11853

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