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.