Théorèmes d'algébricité en géométrie diophantienne
Théorie de l'intersection et théorème de Riemann-Roch arithmétiques
Théorie d'Iwasawa et hauteurs p-adiques.
Theta height and Faltings height
Using original ideas from J.-B. Bost and S. David, we provide an explicit comparison between the Theta height and the stable Faltings height of a principally polarized Abelian variety. We also give as an application an explicit upper bound on the number of -rational points of a curve of genus under a conjecture of S. Lang and J. Silverman. We complete the study with a comparison between differential lattice structures.
Three-dimensional hyperbolic geometry as ...-adic Arakelov geometry.
Uniqueness of equivariant singular Bott-Chern classes
In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic classes, we will see that the construction of Bismut’s equivariant Bott-Chern singular currents provides a unique way to define a theory of equivariant singular Bott-Chern classes. This generalizes J. I. Burgos Gil and R. Liţcanu’s discussion...
Variation of periods modulo in arithmetic dynamics.
Variation of the canonical height on elliptic surfaces I: Three examples.
Weierstrass points on arithmetic surfaces.
ε-constants and equivariant Arakelov–Euler characteristics
О приминении разветвленных накрытий в теории диофантовых уравнений