Desingularization of quasi-excellent schemes in characteristic zero
Desingularization of quasi-excellent schemes in characteristic zero
复制标题
特征零准优方案的去奇异化
DOI：
10.1016/j.aim.2008.05.006
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发表时间：
2007
影响因子：
1.7
通讯作者：
M. Temkin
中科院分区：
文献类型：
--
作者：
M. Temkin
Grothendieck 在 EGA IV 中证明，如果局部诺特格式 X 上的任何有限类型积分格式都承认去奇异化，则 X 是准优秀的，并推测反之亦然。我们用特征零的诺特方案证明了这个猜想。也就是说，从特征零代数簇的奇点解析开始，我们证明了诺特拟优秀Q方案的奇点解析。
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.