Desingularization of quasi-excellent schemes in characteristic zero

Details Desingularization of quasi-excellent schemes in characteristic zero Desingularization of quasi-excellent schemes in characteristic zero

2007-03-22

arxiv.org/abs/math/0703678v2

Advances in Mathematics 219 (2008), pp. 488-522

Mathematics

Algebraic Geometry

35 pages, revised version

Scientific paper

10.1016/j.aim.2008.05.006

Grothendieck proved in EGA IV that if any integral scheme of finite type over a locally noetherian scheme X admits a desingularization, then X is quasi-excellent, and conjectured that the converse is probably true. We prove this conjecture for noetherian schemes of characteristic zero. Namely, starting with the resolution of singularities for algebraic varieties of characteristic zero, we prove the resolution of singularities for noetherian quasi-excellent Q-schemes.

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