Abstract
A local monomialization of an algebraic map between varieties along a valuation is a sequence of blowups of nonsingular subvarieties along the valuation in the domain and target of the map such that the resulting map can be expressed by monomial inclusion in a suitable sense. In this paper we give examples showing that a local monomialization does not always exist over fields of positive characteristic. It was shown in earlier work of the author that a local monomialization always exists over fields of characteristic zero.
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