Integral structures of the Gauss--Manin connection

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Haoyang Guo, University of Minnesota
Fine Hall 224

 Given a proper smooth family of algebraic varieties, its Gauss--Manin connections are fundamental invariants that encode the algebraic/differential information of this family. When the varieties are defined over a p-adic local field and the family has a smooth proper integral model, the Gauss--Manin connections naturally admit integral structures of F-crystals. Yet it is natural to ask if the F-crystals can be constructed independent of choice of models, a conjecture first predicted by Ogus in the 1980s. In this talk, we will explain how the recent advances of p-adic local systems and prismatic formalism offers a solution to this conjecture.