Year: 2003
Type: preprint
Abstract: Using the Frobenius map, we introduce a new invariant for a pair $(R,\a)$ of a ring $R$ and an ideal $\a \subset R$, which we call the F-pure threshold $\mathrm{c}(\a)$ of $\a$, and study its properties. We see that the F-pure threshold characterizes several ring theoretic properties. By virtue of Hara and Yoshida's result, the F-pure threshold $\mathrm{c}(\a)$ in characteristic zero corresponds to the log canonical threshold $\mathrm{lc}(\a)$ which is an important invariant in birational geometry. Using the F-pure threshold, we prove some ring theoretic properties of three-dimensional terminal singularities of characteristic zero. Also, in fixed prime characteristic, we establish several properties of F-pure threshold similar to those of the log canonical threshold with quite simple proofs.
Source: arXiv (Cornell University)
Authors: Takagi, Shunsuke, Watanabe, Kei-ichi
Institutions: Kyushu University, Nihon University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949794496