Hara–Watanabe–Yoshida conjecture on F-rationality of Rees algebras

Let $(R,\mathfrak{m})$ be an excellent $F$-rational local ring, and let $\mathfrak{a}\subseteq R$ be an $\mathfrak{m}$-primary ideal. Define the extended Rees algebra and Rees algebra by

$$T=R[\mathfrak{a}t,t^{-1}],\qquad S=R[\mathfrak{a}t].$$

Hara–Watanabe–Yoshida conjecture. If $T$ is $F$-rational, then $S$ is $F$-rational.

This conjecture concerns the relationship between the $F$-rationality of an extended Rees algebra and its ordinary Rees algebra. Under the stated assumptions, it was first proved by Koley and Kummini, so the conjecture is now a theorem.