Existence of birational small Cohen-Macaulay modules over biquadratic extensions in mixed characteristic

JOURNAL OF ALGEBRA

卷:582

Article

Sridhar, Prashanth¹ 

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

关键词: Birational small Cohen-Macaulay modules;    Biquadratic extensions;    Mixed characteristic;    Unramified regular local ring;    Integral closure;   

DOI  :  10.1016/j.jalgebra.2021.05.002

来源: Elsevier

【 摘 要 】

Let S be an unramified regular local ring of mixed characteristic two and R the integral closure of Sin a biquadratic extension of its quotient field obtained by adjoining roots of sufficiently general square free elements f, g is an element of S. Let S-2 denote the subring of S obtained by lifting to S the image of the Frobenius map on S/2S. When at least one of f, g is an element of S-2, 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 f, g is an element of S-2 or if f, g is not an element of S-2. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free