Higher F-rational singularities

TL;DR

This paper introduces higher F-rationality as a generalization of F-rationality, establishing a connection between characteristic zero and positive characteristic through reduction modulo large primes.

Contribution

It defines higher F-rationality and proves its equivalence to m-rationality in characteristic zero after reduction, also presenting new results on logarithmic extension of forms.

Findings

Normal varieties are m-rational iff m-F-rational after reduction mod p

Established new results on logarithmic extension of forms

Linked characteristic zero properties with positive characteristic via reduction

Abstract

We introduce higher $F$-rationality generalising $F$-rationality. We prove that a normal variety over a field of characteristic zero is $m$-rational if and only if it is $m$-$F$-rational after reduction modulo a sufficiently large prime $p$. Additionally, we establish new results on the logarithmic extension of forms.