代数学コロキウム

開催情報 水曜日　16:40～17:40　数理科学研究科棟(駒場) 056号室 辻 雄

2016年06月08日(水)

16:00-18:30   数理科学研究科棟(駒場) 16:00-17:00は002, 17:30-18:30は056号室
Bruno Kahn 氏 (Institut de mathématiques de Jussieu-Paris Rive Gauche) 16:00-17:00
Torsion order of smooth projective surfaces (English)
[ 講演概要 ]
To a smooth projective variety $X$ whose Chow group of $0$-cycles is $\mathbb{Q}$-universally trivial one can associate its torsion order ${\mathrm{Tor}}(X)$, the smallest multiple of the diagonal appearing in a cycle-theoretic decomposition à la Bloch-Srinivas. We show that ${\mathrm{Tor}}(X)$ is the exponent of the torsion in the Néron-Severi-group of $X$ when $X$ is a surface over an algebraically closed field $k$, up to a power of the exponential characteristic of $k$.
Xu Shen 氏 (Morningside Center of Mathematics) 17:30-18:30
Local and global geometric structures of perfectoid Shimura varieties (English)
[ 講演概要 ]
In this talk, we will investigate some geometric structural properties of perfectoid Shimura varieties of abelian type. In the global part, we will construct some minimal and toroidal type compactifications for these spaces, and we will describe explicitly the degeneration of Hodge-Tate period map at the boundaries. In the local part, we will show that each Newton stratum of these perfectoid Shimura varieties can be described by the related (generalized) Rapoport-Zink space and Igusa variety. As a consequence of our local and global constructions, we can compute the stalks of the relative cohomology under the Hodge-Tate period map of the intersection complex (on the minimal compactification), in terms of cohomology of Igusa varieties at the boundary with truncated coefficients.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.今回は北京からの中継です．)