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ミニ研究集会「数論幾何とその周辺」




日程
2010年7月19日(月,
注意:7月19日は国民の祝日(海の日)です.
場所
京都大学理学研究科数学教室 理学部3号館108教室
(北部構内マップ)
講演者
加藤和也 (シカゴ大学)
Luc Illusie (パリ南大学/東京大学)
臼井三平 (大阪大学)
Mohamed Saidi (エクセター大学/京大数理研)
Anna Cadoret (I.B.M. - ボルドー第1大学)
世話人・連絡先
玉川安騎男(京大数理研)
伊藤哲史(京大数学教室) (e-mail: my first name at math.kyoto-u.ac.jp)

プログラム

PDF version: [日本語版], [英語版]

10:00-11:00 11:10-12:10 14:00-15:00 15:30-16:30 16:40-17:40
7月19日(月, 加藤 Illusie 臼井 Saidi Cadoret

7月19日(月,
10:00-11:00加藤和也 (シカゴ大学)
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.
11:10-12:10Luc Illusie (パリ南大学/東京大学)
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) = Πρlk), 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臼井三平 (大阪大学)
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)
15:30-16:30Mohamed Saidi (エクセター大学/京大数理研)
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.
16:40-17:40Anna Cadoret (I.M.B. - ボルドー第1大学)
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 := ρM1(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-(懇親会)


最終更新日:2010年6月28日(月)