Study of Noetherian local rings in commutative algebra

混合特征局部环上大Cohen-Macaulay模的构造：H.Bass和M.Auslander提出的关于Noether局部环上有限生成模的猜想称为同调猜想。许多交换代数学家对这个问题进行了研究。M.Hochster证明了大Cohen-Macaulay模的存在蕴含了猜想，并成功地证明了等特征局部环上的大Cohen-Macaulay模的存在性。我们得到了混合特征局部环上的结果。

Construction of big Cohen-Macaulay modules over mixed characteristic local rings : The conjectures on finitely generated modules over Noetherian local rings asked by H.Bass and M.Auslander are called "Homological Conjectures". Many commutative algebraists have studied on this subject. M.Hochster showed that the existence of big Cohen-Macaulay modules implies the conjectures and succeeded to show the existence over equal characteristic local rings. We have got the result over mixed characteristic local rings.