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

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.

Title changed, an enlarged version containing the result of previous version

References in corpus (3)

• Singularities in arbitrary characteristic via jet schemes
• Log canonical thresholds in positive characteristic
• Finite determination conjecture for Mather-Jacobian minimal log discrepancies and its applications