Abstract
Our main result establishes functorial desingularization of noetherian quasi-excellent schemes over Q with ordered boundaries. A functorial embedded desingularization of quasi-excellent schemes of characteristic zero is deduced. Furthermore, a standard simple argument extends these results to other categories including, in particular, (equivariant) embedded desingularization of the following objects of characteristic zero: qe algebraic stacks, qe formal schemes, complex and non-archimedean analytic spaces. We also obtain a semistable reduction theorem for formal schemes.
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Temkin, M. Functorial desingularization over Q: boundaries and the embedded case. Isr. J. Math. 224, 455–504 (2018). https://doi.org/10.1007/s11856-018-1656-6
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DOI: https://doi.org/10.1007/s11856-018-1656-6