Resolution of singularities of threefolds in positive characteristic. I.: Reduction to local uniformization on Artin–Schreier and purely inseparable coverings

168 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Resolution of singularities of arithmetical threefolds (2014, unknown): “This allows us to adapt the techniques developed in [29] [30].”
Inseparable local uniformization (2008, methodology): “ong. Perhaps, one can divide these works to three classes. (i) Pushing existing techniques to their limit. I expect that the following two problems can be solved in this way: (a) extend the method of [CP1] to desingularize any scheme of dimension 3 that admits a morphism of ﬁnite type to an excellen”
On the rationality of Kawamata log terminal singularities in positive characteristic (2017, background): “nd (Y,Supp(f−1(D) + Exc(f))) has simple normal crossings (see [Kol13, Deﬁnition 1.8 and 1.12]). If X is of dimension at most three, then a log resolution of (X,D) always exists (see [Lip78], [Cut09], [CP08], and [CP09]). Theorem 2.1 ([Kol13, Theorem 10.4]). Let X be a regular surface over a ﬁeld kan”
Singularities in positive characteristic, stratification and simplification of the singular locus (2008, background): “ late eighties ([6], [11], [16], [26], [29], [30], [34]). There are some results on low dimensional varieties over arbitrary ﬁelds by Abhyankar, and more recently by some other authors (see also [7], [8]), [9]), [10]) but the general question of resolution remains open. Another important contributio”