Biography

Research topic

Key words: Abelian varieties, arithmetic D-modules, cristalline D-modules, Fourier-Mukai transform, rigid analytic varieties.

In 1981, Shigeru Mukaï defined the now called Fourier-Mukaï transform for abelian varieties over algebraically closed fields, which gives an equivalence of categories between quasi-coherent sheaves over an abelian variety and quasi-coherent sheaves over its dual. It has some important applications in other domains such as mirror symmetry and string theory.

Thanks to the independent work of Laumon and Rothstein, the construction of the Fourier-Mukaï transform have been extended to sheaves of differential operators on a locally noetherian base of characteristic zero, using the universal vectorial extension of the dual of an abelian variety.

The goal of my research is to define similar transforms in the arithmetic case, using the arithmetic sheaves of differential operators introduced by Berthelot. This induces, among others, a deep comprehension of the Poincaré sheaf and the construction of an arithmetic group scheme analogous to the universal vectorial extension of the dual abelian variety.