Small rational points on elliptic curves over number fields.
Global minimal models for endomorphisms of projective space
We prove the existence of global minimal models for endomorphisms of projective space defined over the field of fractions of a principal ideal domain.
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.
Page 1