The chromatic tower for D(R)
The chromatic tower for D(R)
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DOI：
10.1016/0040-9383(92)90047-l
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发表时间：
1992-07
期刊：
影响因子：
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通讯作者：
A. Neeman;M. Bökstedt
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文献类型：
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作者：
A. Neeman;M. Bökstedt
按照代数学家的约定，我们称D*（R）的三角化子范畴为epaisse，如果它们在直和项下是满的和闭的。霍普金斯定理是一个美丽的结果。除此之外，它还确定了从一些看似无意义的东西中，比如R的派生范畴，人们可以恢复一个非常有意义的对象，比如Spec（R）。然而，在证据上有一个差距。如果没有一些额外的假设（如R诺特）的定理是假的。在第4节中可以找到一个反例。我应该立即补充说，霍普金斯是通过研究拓扑环境中的类似性质而得到他的结果的，在[6]中得到了一些真正显著而有力的结果。上述定理出现在一份文件中的会议记录，他解释了拓扑结果，并指出，通过代数模拟也是正确的。应该强调的是，霍普金斯的结果是非常有趣的，可能是非常重要的。他发现了稳定同伦理论和代数几何之间的平行，这种平行应该进一步探索。这也许是适当的一点，以简要概述我们在这里所做的拓扑平行。我们的出发点（这在历史上是完全错误的）是CmSo可以被赋予Em环谱的结构。因此，在某种意义上，它可以被视为交换环，人们可能希望研究这个好奇的代数几何。
Following the conventions of algebraists, we will call triangulated subcategories of D*(R) epaisse if they are full and closed under direct summands. Hopkins’ theorem is a beautiful result. Among other things, it establishes that out of something seemingly nonsensical, like the derived category of R, one can recover a very sensible object, like Spec (R). However, there is a gap in the proof. Without some added hypotheses (eg R Noetherian) the theorem is false. A counterexample may be found in Section 4.I should immediately add that Hopkins obtained his result by studying analogous properties in the topological setting, where [6] obtained some really remarkable and powerful results. The theorem quoted above occurs in a paper in a conference proceedings, where he explained the topological result and remarked in passing that the algebraic analogue is also correct. It should be stressed that Hopkins’ result is very intriguing, and possibly very important. He discovered a parallel between stable homotopy theory and algebraic geometry, and this parallel should be explored further. This is perhaps the appropriate point to briefly outline the topological parallel of what we do here. The starting point for us (this is historically quite wrong) is that CmSo can be given the structure of an Em ring spectrum. Therefore, in some sense it may be viewed as a commutative ring, and one may wish to study the algebraic geometry of this curious