On 𝑝_{𝑔}-ideals in positive characteristic

Abstract

Let ( A , m ) (A,\mathfrak {m} ) be an excellent normal domain of dimension two containing a field k ≅ A / m k \cong A/\mathfrak {m} . An m \mathfrak {m} -primary ideal I I is a p g p_g -ideal if the Rees algebra A [ I t ] A[It] is a Cohen-Macaulay normal domain. If k k is algebraically closed then Okuma, Watanabe and Yoshida proved that A A has p g p_g -ideals and furthermore product of two p g p_g -ideals is a p g p_g ideal. Previously we showed that if k k has characteristic zero then A A has p g p_g -ideals. In this paper we prove that if k k is perfect field of positive characteristic then also A A has p g p_g ideals.