日時：2004年1月29日（木）〜31日（金）
場所：東北大学理学部（青葉山キャンパス）川井ホール
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プログラム
１月２９日 (木)
13:00--15:00 Y. Andr\'e 氏
連続講義 I15:30--17:00 都築 暢夫 氏
TBATea time
１月３０日 (金)
10:00--12:00 Y. Andr\'e 氏
連続講義 II13:30--15:00 斎藤 秀司 氏
Cycle class map for arithmetic schemes15:30--17:00 加藤 文元 氏
On degeneration of restrained ramifications18:00-- 懇親会
１月３１日 （土）
10:00--12:00 Y. Andr\'e 氏
連続講義 III
13:30--15:00 木村 俊一 氏
Alexander property is etale local
15:30--17:00 織田 孝幸 氏
The known and the unknown on Fourier expansions of automorphic forms
1) On finite-dimensional motives
Since Mumford's work, it is well-known that Chow groups of projective varieties are of infinite type in general, in a very strong sense. Nevertheless, S.-I. Kimura and P. O'Sullivan have conjectured independently that Chow motives are of ``finite dimension", in the sense that, like super-vector bundles, they can be expressed as the sum of an even summand (of which some exterior power vanishes) and an odd summand (of which some symmetric power vanishes). I'll present some aspects of this (categorical) notion of finite-dimensionality, notably part of O'Sullivan's theory, relations with other conjectures (Bloch-Beilinson-Murre, Voevodsky), and applications (abelian varieties...).
2) On the theory of motivated cycles and applications
I'll review two ways of getting around the standard conjectures in some problems concernig pure motives. One of them was developped in my IHES 63's paper, over a field $K$ of char. 0. We fix a family $\mathcal V$ of smooth projective varieties, and call motivated any rational cohomology class on some $X$ in $\mathcal V$ which belongs to the smallest family which contains (classes of) algebraic cycles, is stable by pull-back and enjoys the following property: the cohomology classes fixed by the subgroup of $GL(H(X))$ which fixes any given set of motivated cycles are all motivated. It turns out that there is a ``formula" for motivated cycles, that they give rise to a tannakian category of motives, and that they are stable by parallel transport (provided $\mathcal V$ is big enough). I'll then discuss the situation in characteristic $p$ (recent results), and outline applications to abelian varieties.
研究集会世話人 :東北大学理学研究科数学教室
花村 昌樹 (Tel. 022-217-6386, e-mail: hanamura@math.tohoku.ac.jp)