专业化条件下本质维度的行为

Pub Date : 2021-12-23 DOI:10.46298/epiga.2022.8910

Z. Reichstein, F. Scavia

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引用次数: 4

摘要

设$A$是一个具有一般点$\eta$和闭点$s$的离散估值环。我们证明了在$\operatorname{Spec}(a)$上的一组环量中，$ $s$上的环量的本质维数小于或等于$ $\eta$上的环量的本质维数。我们给出了这一结果的两种应用，一种应用于混合特性，另一种应用于等特性。

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The behavior of essential dimension under specialization

Let $A$ be a discrete valuation ring with generic point $\eta$ and closed point $s$. We show that in a family of torsors over $\operatorname{Spec}(A)$, the essential dimension of the torsor above $s$ is less than or equal to the essential dimension of the torsor above $\eta$. We give two applications of this result, one in mixed characteristic, the other in equal characteristic.

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