A criterion for rational places over local fields.
A note on Waring's problem in p-adic fields
A p-adic Perron-Frobenius theorem
We prove that if an n×n matrix defined over ℚ ₚ (or more generally an arbitrary complete, discretely-valued, non-Archimedean field) satisfies a certain congruence property, then it has a strictly maximal eigenvalue in ℚ ₚ, and that iteration of the (normalized) matrix converges to a projection operator onto the corresponding eigenspace. This result may be viewed as a p-adic analogue of the Perron-Frobenius theorem for positive real matrices.
Adeles and differential forms.
Algebraic Weyl system and application
Approximations diophantiennes et problèmes additifs dans les groupes abéliens localement compacts