Israel Journal of Mathematics

, Volume 224, Issue 1, pp 455–504 | Cite as

Functorial desingularization over Q: boundaries and the embedded case

  • Michael Temkin


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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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsThe Hebrew University of JerusalemGiv’at Ram, JerusalemIsrael

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