The \(\operatorname{arc}\)-topology
The paper under review aims to study a new Grothendieck topology on the category of quasi-compact quasi-separated schemes, the so-called arc-topology. It is a slight refinement of the v-topology and h-topology for more general non-noetherian schemes. Covers in the arc-topology are tested via rank \(\leq 1 \) valuation rings. Examples of arc sheaves include étale cohomology with torsion coefficients and perfect complexes on perfect \(\mathbb{F}_p\)-schemes. Using the arc-desent, Bhatt (the first author) and Scholze established the étale comparison theorem for prismatic cohomology. As applications, the authors reproved two classical results in étale cohomology: (i) the Gabber-Huber affine analog of proper base change theorem; (ii) the Fujiwara-Gabber theorem for punctured henselian pairs. They also gave an application to Artin-Grothendieck's vanishing theorem in rigid analytic geometry, which strengthens the results of \textit{D. Hansen} [Compos. Math. 156, No. 2, 299--324 (2020; Zbl 1441.14085)].
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