TY - JOUR
T1 - Functorial desingularization over Q
T2 - boundaries and the embedded case
AU - Temkin, Michael
N1 - Publisher Copyright:
© 2018, Hebrew University of Jerusalem.
PY - 2018/4/1
Y1 - 2018/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85046643664&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1656-6
DO - 10.1007/s11856-018-1656-6
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AN - SCOPUS:85046643664
SN - 0021-2172
VL - 224
SP - 455
EP - 504
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -