$F$-rationality of Rees algebras

TL;DR

This paper investigates the $F$-rationality properties of Rees algebras associated with $rak{m}$-primary ideals in excellent local rings of prime characteristic, addressing open conjectures in the field.

Contribution

It provides partial answers to existing conjectures about the $F$-rationality of Rees algebras in prime characteristic rings.

Findings

Established conditions under which Rees algebras are $F$-rational.

Partially confirmed conjectures posed by Hara, Watanabe, and Yoshida.

Extended understanding of $F$-rationality in the context of local algebra.

Abstract

In this paper, we study the $F$-rationality of the Rees algebra and the extended Rees algebra of $\mathfrak{m}$-primary ideals in excellent local rings $(R, \mathfrak{m})$ of prime characteristic. We partially answer some conjectures and questions raised by N. Hara, K.-i. Watanabe and K.-i. Yoshida (J. Algebra, pp.153--190, vol 247, 2002).