Resolution of singularities in arbitrary characteristic

我们的目标是解决任意特征(或者更一般地，混合特征)中的奇点。在该基金的帮助下，调查人员围绕这一问题得出了各种结果。库拉诺用亚当斯的行动描述了本土化的陈冠希角色，这是由于吉利索尔。利用它证明了duta重数的正性，并且如果两个模中的一个是等特征Roberts环上的Cohen-Macaulay模，则由此得到与Serre正性相同的结果。Kawasaki证明了任意方案的Cohen-Macaulay化的存在性。根据这一结果，在构造奇点分解时，我们可以假定所给格式是Cohen-Macaulay格式。Ito构造了三维McKay对应。Oka使用分解圆环簇奇点的方法来研究弯曲曲线。Terao通过计算单行来研究超平面排列。Nakamura研究了如何使用计算机计算显式示例。武田研究了Grothendieck提出的标准猜想。由于富尔顿-麦克弗森，横仓使用等变理论来研究米尔纳班级。石川研究了空间曲线的切可展性。Fukui证明了一些在太阳性理论中很重要的环的Cohen-Macaulay性。

Our aim was to make resolution of singularities in arbitrary characteristic (or, more generally, in mixed-characteristic). By the help of the fund, investigators have got various results around the problem. Kurano described localized Chern characters in terms of Adams operations due to Gillet-Soule. Using it, the positivity of Dutta multiplicity was proven, and if one of two module is Cohen-Macaulay over a Roberts ring of equi-characteristic, then the same result as Serre's positivity follows from it. Kawasaki proved the existence of Cohen-Macaulayfication for arbitrary schemes. By the result, we may assume that the given scheme is Cohen-Macaulay when we construct resolution of singularity. Ito constructed 3-dimensional McKay correspondence. Oka studies flex curves using the method of resolution of singularities of toric varieties. Terao studied hyperplane arrangement by calculating monodromy. Nakamura studied how to compute explicit examples using computers. Takeda studied the standard conjecture due to Grothendieck. Yokura studied Milnor classes using equivariant theory due to Fulton-MacPherson. Ishikawa studied the tangent developables of space curves. Fukui proved the Cohen-Macaulayness for some rings that are important in sungularity theory.