| Description: | [DMS Seminar] Arnab Saha (Australian National University) -- Differential Isocrystals Associated to Abelian Schemes |
| Date: | Wednesday, Mar 28, 2018 |
| Time: | 11:30 a.m. - 12:30 p.m. |
| Venue: | 110, Lecture Hall Complex |
| Details: | The main aim of this talk is to construct a canonical F-isocrystal H(A) for an abelian scheme A over a p-adic complete discrete valuation ring of perfect residue field. This F-isocrystal H(A) comes with a Hodge-type filtration and admits a natural map to the usual Hodge sequence of A. Even though H(A) admits a map to the crystalline cohomology of A, the F-structure on H(A) is fundamentally distinct from the one on the crystalline cohomology of A. The weak admissibility of H(A), when A is an elliptic curve, 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). This is joint work with Jim Borger and the talk will be self-contained explaining all the necessary ideas. |
| Calendar: | Seminar Calendar (entered by saugata.bandyopadhyay) |