| Résume | From a model theoretic point of view, local fields of positive characteristic, i.e. fields of Laurent series over finite fields, are much less well understood than their characteristic zero counterparts - the fields of real, complex and p-adic numbers. I will discuss different approaches to axiomatize and decide at least their existential theory in various languages and under various forms of resolution of singularities. From a geometric point of view, deciding the existential theory essentially means to determine algorithmically which algebraic varieties have rational points over these fields.
Joint work with Sylvy Anscombe and Philip Dittmann.
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