Geometric proofs of theorems of Ax-Kochen and Ersov

Jan Denef

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arXiv · 1601.03607

Geometric proofs of theorems of Ax-Kochen and Ersov

Jan Denef

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Abstract

We give an algebraic geometric proof of the Theorem of Ax and Kochen on p-adic diophantine equations in many variables. Unlike Ax-Kochen's proof, ours does not use any notions from mathematical logic and is based on weak toroidalization of morphisms. We also show how this geometric approach yields new proofs of the Ax-Kochen-Ersov transfer principle for local fields, and of quantifier elimination theorems of Basarab and Pas.

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Jan Denef. 2016-01-14. Geometric proofs of theorems of Ax-Kochen and Ersov. https://arxiv.org/abs/1601.03607

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