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Existence of birational small Cohen-Macaulay modules over biquadratic extensions in mixed characteristic
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-05-07 , DOI: 10.1016/j.jalgebra.2021.05.002 Prashanth Sridhar
中文翻译:
具有混合特征的双二次扩展上的双理性小Cohen-Macaulay模的存在
更新日期:2021-05-12
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-05-07 , DOI: 10.1016/j.jalgebra.2021.05.002 Prashanth Sridhar
Let S be an unramified regular local ring of mixed characteristic two and R the integral closure of S in a biquadratic extension of its quotient field obtained by adjoining roots of sufficiently general square free elements . Let denote the subring of S obtained by lifting to S the image of the Frobenius map on . When at least one of , we characterize the Cohen-Macaulayness of R and show that R admits a birational small Cohen-Macaulay module. It is noted that R is not automatically Cohen-Macaulay in case or if .
中文翻译:
具有混合特征的双二次扩展上的双理性小Cohen-Macaulay模的存在
设S为混合特征2的无分支规则局部环,R为S的商因数的二次封闭式中的S的整体闭环,该商数是通过邻接足够普通的方形自由元素的根获得的。让表示通过将Frobenius映射图上的图像提升至S而获得的S的子环。。当至少一项,我们刻画了R的Cohen-Macaulayness的特征,并证明R接受了双边小Cohen-Macaulay模块。请注意,如果出现以下情况,R不会自动成为Cohen-Macaulay 或者如果 。