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

[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.

[发布日期] 2021-12-01

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