  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.
