Chennai Mathematical Institute


3:30 pm, Lecture Hall 3
Isocrystals associated to arithmetic jet spaces of abelian schemes

Arnab Saha
Australian National University.


The main aim of this talk is to construct a canonical F-isocrystal H(A)_K for an abelian scheme A over a p-adic complete discrete valuation ring of perfect residue field K. This F-isocrystal H(A)_K comes with a filtration and admits a natural map to the usual Hodge sequence of A. Even though H(A)_K admits a map to the crystalline cohomology of A, the F-structure on H(A)_K is fundamentally distinct from the one on the crystalline cohomology. When A is an elliptic curve, we further show that H(A) itself is an F-crystal and that implies a strengthened version of Buium?s result on differential characters. The weak admissibility of H(A) depends on a modular parameter over the points of the moduli of elliptic curves. Hence the Fontaine functor associates a new p-adic Galois representation to every such weakly admissible F-crystal H(A).