Differential characters and characteristic polynomial of Frobenius.
Differential characters of abelian varieties over p-adic fields.
Fields of definition of algebraic varieties in characteristic zero
Uniform bound for generic points of curves in tori.
Degree of the fibres of an elliptic fibration
Let an elliptic fibration with general fibre . Let be the minima of the non-zero intersection numbers where runs successively through the following sets: effective divisors on , invertible sheaves spanned by global sections, ample divisors and very ample divisors. Let be the maximum of the multiplicities of the fibres of . We prove that if and only if and that if and only if .
Killing divisor classes by algebraisation
It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.
Differential overconvergence
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation". This property can be viewed as a special kind of overconvergence property. One can also go in the opposite direction by using differential functions that arise in a ramified situation to construct "new" (unramified) differential functions.
Reduction of the Manin map modulo p.
Lang’s conjecture in characteristic : an explicit bound
Integral points of abelian varieties over function fields of characteristic zero.
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.
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