Prof. Dr. Gerd Faltings

Biography

1978 PhD, University of Münster 1978 - 1979 Visitor, Harvard University, Cambridge, MA, USA 1979 - 1982 Assistant Professor, University of Münster 1981 Habilitation, University of Münster 1982 - 1984 Professor, University of Wuppertal 1985 - 1994 Professor, Princeton University, NJ, USA Since 1994 Scientific Member, Max Planck Institute for Mathematics, Bonn Since 1995 Director, Max Planck Institute for Mathematics, Bonn Diophantine equations  Arakelov theory  Abelian varieties  Moduli spaces of vectorbundles  p-adic Hodge theory

Research Interest

Former Research Area D I have found a crystalline version of nonabelian p-adic Hodge theory for ‘small’ representations. Motivic cohomology and Diophantine equations: Kim has introduced a new method into Diophantine approximation. The paper [1] constructs a motivic logarithm for arbitrary curves. An open question is the construction of such an object in algebraic K-theory, as well as a good definition of torsors over it. Former Research Area E Using the Hitchin fibration, the dimension of global sections for line-bundles of central charge one on moduli spaces of G-bundles has been computed in [2]. In [3], I determined the image of the Rapoport-Zink period map in the case of GL(n), confirming conjectures of Hartl and Rapoport-Zink. Research Area DE I extended the definition of the category MF to the semistable case. As an application I could construct semistable models for certain Shimura-varieties defined by Spin-groups with level-structure, see [4]. I also obtained estimates for the norms of Weierstrass-sections on curves.