标题： 正则环上完美复形范畴的 Rouquier 维数 显示英文标题

标题： The Rouquier dimension of the category of perfect complexes over a regular ring

摘要： 我们证明了在正则环上完美复形范畴的Rouquier维数恰好等于该环的克鲁尔维数。 以前，已知克鲁尔维数是一个上界，但一般情况下下界并不为人所知。 特别是，对于正则局部环，这个结果是新的。 更一般地，我们证明了Rouquier维数的下界由最长正则序列的长度给出。 显示英文摘要

摘要： We show that the Rouquier dimension of the category of perfect complexes over a regular ring is precisely the Krull dimension of the ring. Previously, it was known that the Krull dimension is an upper bound, the lower bound however was not known in general. In particular, for regular local rings this result is new. More generally, we show that a lower bound of the Rouquier dimension is given by the maximal length of a regular sequence.