论文标题
在某些零维方案上的相干滑轮的派生类别
Derived categories of coherent sheaves on some zero-dimensional schemes
论文作者
论文摘要
令$ x_n $为$ n $二维仿射空间的封闭点的第二个无穷小社区。在本说明中，我们研究了$ d^b（coh \，x_n）$，这是$ x_n $上有限的相干滑轮类别。我们表明，对于$ n \ geq 2 $，与零维完成交集的情况相反，$ d^b（coh \，x_n）中的三角形子类别的晶格具有丰富的结构（可能是野生的）。我们还建立了$ d^b（coh \，x_n）$中的三角形子类别与$ n $变量中免费分级的关联代数的通用本地化之间的关系。我们的同源方法为这种普遍定位的结构提供了一些应用。
Let $X_N$ be the second infinitesimal neighborhood of a closed point in $N$-dimensional affine space. In this note we study $D^b(coh\, X_N)$, the bounded derived category of coherent sheaves on $X_N$. We show that for $N\geq 2$ the lattice of triangulated subcategories in $D^b(coh\, X_N)$ has a rich structure (which is probably wild), in contrast to the case of zero-dimensional complete intersections. We also establish a relation between triangulated subcategories in $D^b(coh\, X_N)$ and universal localizations of a free graded associative algebra in $N$ variables. Our homological methods produce some applications to the structure of such universal localizations.
