Inversion of modulo p reduction and a partial descent from characteristic 0 to positive characteristic

TL;DR

This paper introduces a method called 'lifting to characteristic 0' to invert modulo p reduction, enabling the descent of conjectures and bounds from characteristic 0 to positive characteristic for certain pairs.

Contribution

It presents a novel 'lifting to characteristic 0' technique that facilitates the transfer of key conjectures and bounds from characteristic zero to positive characteristic settings.

Findings

Mustata-Nakamura's conjecture descends to positive characteristic for certain pairs.

Uniform bounds of divisors computing log canonical thresholds are established in positive characteristic.

The paper proposes a problem whose solution would extend these results to all pairs.

Abstract

In this paper we focus on pairs consisting of the affine $N$-space and multiideals with a positive exponent. We introduce a method "lifting to characteristic 0" which is a kind of the inversion of "modulo p reduction". By making use of it, we prove that Mustata-Nakamura's conjecture and some uniform bound of divisors computing log canonical thresholds descend from characteristic 0 to certain classes of pairs in positive characteristic. We also pose a problem whose affirmative answer gives the descent of the statements to the whole set of pairs in positive characteristic.