Abstract
AbstractWe investigate the geometry of finite maps and correspondences between curves, and construct canonical trace and pullback maps between Hyodo–Kato integral structures on de Rham cohomology of curves, which are functorial for finite morphisms of the generic fibres. This leads to a crystalline version of the étale cohomology of towers of modular curves considered by Hida and Ohta, whose ordinary part satisfies $\Lambda $-adic control and Eichler–Shimura theorems.
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