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| 10:00-11:00 | 11:10-12:10 | 14:00-15:00 | 15:30-16:30 | 16:40-17:40 | |
|---|---|---|---|---|---|
| July 19 (Mon) | Kato | Illusie | Usui | Saidi | Cadoret |
| July 19 (Mon), 2010 | |
| 10:00-11:00 | Kazuya Kato (Chicago) |
| Moduli spaces of log mixed Hodge structures and application to construction of Néron models, I (joint work of K. Kato, C. Nakayama, and S. Usui) | |
Abstract: We construct toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are fine moduli spaces of log mixed Hodge structures with polarized graded quotients. We also apply them to construct Néron models of intermediate Jacobians over higher dimensional bases. | |
| 11:10-12:10 | Luc Illusie (Paris-Sud/Tokyo) |
| Independence of families of l-adic representations, after J.-P. Serre | |
Abstract: Let k be a number field, k an algebraic closure of k, Γk = Gal(k/k). A family of continuous homomorphisms ρl : Γk → Gl, indexed by prime numbers l, where Gl is a locally compact l-adic Lie group, is said to be independent if ρ(Γk) = Πρl(Γk), where ρ = (ρl) : Γk → ΠGl. Serre gave a criterion for such a family to become independent after a finite extension of k. I will explain Serre's criterion and show that it applies to families coming from the l-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over k. | |
| 14:00-15:00 | Sampei Usui (Osaka) |
| Moduli spaces of log mixed Hodge structures and application to construction of Néron models, II (joint work of K. Kato, C. Nakayama, and S. Usui) | |
| 15:30-16:30 | Mohamed Saidi (Exeter/Kyoto RIMS) |
| Fake liftings of Galois covers between smooth curves | |
Abstract: We introduce the notion of fake liftings of cyclic covers between smooth curves, which only exist if the Oort conjecture on liftings of cyclic covers between smooth curves is false, and establish some of their basic properties. | |
| 16:40-17:40 | Anna Cadoret (Bordeaux 1) |
| On the Galois module structure of the generic l-torsion of an abelian scheme (joint work with Akio Tamagawa) | |
Abstract: Let k be a field of characteristic 0, S a smooth, separated, geometrically connected curve over k with generic point η and A → S an abelian scheme. Let π1(S) denote the étale fundamental group of S. Then, for each prime l, one gets the natural representation: ρl : π1(S) → GL(Aη[l]). Via the theory of étale fundamental groups, one can associate to this representation curves which are natural generalizations of the classical modular curves Y(l), Y1(l) and which we call abstract modular curves. The structure of Aη[l] as a π1(S)-module encodes lots of information about abstract modular curves. A key result is the following. Given a π1(S)-submodule M ⊆ Aη[l], write ρM: π1(S) → GL(M) for the induced representation and set GM := ρM(π1(S)). Then: (1) Aη[l] is a semisimple π1(S)-module, l >> 0. (2) There exists an integer B = B(A) ≥ 1 such that for any prime l, π1(S)-submodule M ⊆ Aη[l] and any abelian normal subgroup C \vartriangleleft GM, |C| ≤ B. I will sketch the proof of this statements and, if I have time, explain how to derive from it estimates for the genus and gonality of abstract modular curves when l >> 0. | |
| 19:00- | (Banquet) |