Moduli of geometric objects and period maps into spaces of linear structures play a central role in geometry and arithmetic. A main source of period maps in positive characteristic is given by additional structures on the crystalline cohomology of algebraic varieties. In this project we want to focus on display structures. As a starting point we consider the period map from the space of truncated Barsotti-Tate groups into the space of truncated (standard) displays. We ask how much information can be recovered from this map. Moreover, we want to develop a theory of truncated G-displays for a linear algebraic group G, study the moduli spaces of these objects, and define and study period morphisms into these spaces. We expect applications for example to reductions of PEL Shimura varieties and to K3 surfaces.
DFG Programme
Research Grants
