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Article Dans Une Revue Forum of Mathematics, Sigma Année : 2023

Hensel minimality II: Mixed characteristic and a diophantine application

Résumé

We extend the results about Hensel minimality to include also the mixed characteristic case. This completes our axiomatic framework for tame non-archimedean geometry over Henselian valued fields of characteristic zero. We prove a Jacobian property, a strong form of Taylor approximations of definable functions, resplendency results and cell decomposition, all under 1-h-minimality. We obtain a diophantine application of counting rational points of bounded height on Hensel minimal curves.

Dates et versions

hal-03332241 , version 1 (02-09-2021)

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Raf Cluckers, Immanuel Halupczok, Silvain Rideau-Kikuchi, Floris Vermeulen. Hensel minimality II: Mixed characteristic and a diophantine application. Forum of Mathematics, Sigma, In press. ⟨hal-03332241⟩
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