论文标题
依次横向理想产物的Avramov障碍物消失
Vanishing of Avramov Obstructions for Products of Sequentially Transverse Ideals
论文作者
论文摘要
如果$ i \ cap j = ij $，则两个理想$ i $和$ j $称为横向。我们表明，Avramov定义的障碍物针对常规本地戒指（依次）横向理想的类别总是$ 0 $。特别是，我们为所有这些理想计算明确的自由分辨率和Koszul同源性。此外，我们在相关的Koszul络合物上构建了一个显式的Massey操作，因此（通过Golod的构造）在横向理想的乘积定义的商标上，将残留场的自由分辨率最少。我们以有关关联乘法结构的存在的问题进行了疑问，该结构在最小的自由分辨率上的最小解析是由横向理想产物定义的。
Two ideals $I$ and $J$ are called transverse if $I \cap J = IJ$. We show that the obstructions defined by Avramov for classes of (sequentially) transverse ideals in regular local rings are always $0$. In particular, we compute an explicit free resolution and Koszul homology for all such ideals. Moreover, we construct an explicit trivial Massey operation on the associated Koszul complex and hence (by Golod's construction) a minimal free resolution of the residue field over the quotient defined by the product of transverse ideals. We conclude with questions about the existence of associative multiplicative structures on the minimal free resolution of the quotient defined by products of transverse ideals.
