On the existence of birational maximal Cohen-Macaulay modules over biradical extensions in mixed characteristic

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Sridhar, Prashanth¹ 

[1] Univ Kansas, 405 Snow Hall,1460 Jayhawk Blvd, Lawrence, KS 66045 USA

关键词: Birational maximal Cohen-Macaulay module;    Biradical extension;    Mixed characteristic;    Unramified regular local ring;    Integral closure;   

DOI  :  10.1016/j.jpaa.2021.106790

来源: Elsevier

【 摘 要 】

Let S be an unramified regular local ring of mixed characteristic p >= 3 and S-p the subring of Sobtained by lifting to Sthe image of the Frobenius map on S/pS. Let Rbe the integral closure of Sin a biradical extension of degree p2of its quotient field obtained by adjoining p-th roots of sufficiently general square free elements f, g is an element of S-p. We show that Radmits a birational maximal Cohen-Macaulay module. It is noted that Ris not automatically Cohen-Macaulay. (c) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free