将概型提升到谱概型的一个障碍
An obstruction to lifting schemes to spectral schemes
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中文总结 AI 辅助
研究将整数上概型提升到球谱上谱概型的障碍，扩展尼古劳斯关于环的结果，证明\(\hat\delta\)-环相关性质及定义\(\hat\delta\)-概型，还应用于数环等具体例子。
中文摘要 AI 辅助
我们开发并研究了一个将整数上的概型提升到球谱上的谱概型的障碍。这扩展了尼古劳斯关于环的一个结果，该结果表明可提升性的一个必要条件是存在一个\(\hat\delta\)-结构。我们证明了\(\hat\delta\)-环的下降性质，定义了\(\hat\delta\)-概型，并证明了一个类似的陈述。然后我们将其应用于具体例子，如数环、\(\mathbb P^n\)的闭子概型和各种群概型。
英文摘要
$\hatδ$-rings are a globalization of $δ$-rings. Motivated by their application to obstructing spectral lifts, we develop the theory of animated $\hatδ$-rings. They extend the discrete notion in the same way that animated $δ$-rings extend that of $δ$-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.
