Proof of a conjecture of Colliot-Thélène

Mathematics – Algebraic Geometry

Scientific paper

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14 pages

Scientific paper

We prove a conjecture of Colliot-Th\'el\`ene that implies the Ax-Kochen
Theorem on p-adic forms. We obtain it as an easy consequence of a diophantine
purity theorem whose proof forms the body of the present paper.

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