In mathematics, especially in algebraic geometry, the v-topology (also known as the universally subtrusive topology) is a Grothendieck topology whose covers are characterized by lifting maps from valuation rings.
, the normalisation of the cusp, and the Frobenius in positive characteristic are v-coverings.
See h-topology, relation to the v-topology Bhatt & Mathew (2018) have introduced the arc-topology, which is similar in its definition, except that only valuation rings of rank ≤ 1 are considered in the definition.
A variant of this topology, with an analogous relationship that the h-topology has with the cdh topology, called the cdarc-topology was later introduced by Elmanto, Hoyois, Iwasa and Kelly (2020).
[1] Bhatt & Scholze (2019, §8) show that the Amitsur complex of an arc covering of perfect rings is an exact complex.