Date: 25(Mon)-29(Fri)/Sep/2006

Place: Graduate School of Mathematics, University of Tokyo, Komaba, Meguro-ku, Tokyo, Japan,

Organizers:

S. Kimura (Hiroshima University)

A. Shiho (University of Tokyo), G. Yamashita (RIMS)

Speakers:

M. Asakura (Kyushu University)

K. Hagihara (University of Tokyo)

Y. Hashimoto (Osaka City University)

A. Ikeda (Osaka University)

K. Kimura (Tsukuba University)

S. Kimura (Hiroshima University)

K. Kurano (Meiji University)

N. Minami (Nagoya Institute of Technology)

S. Mochizuki (University of Tokyo)

A. Pal (IHES)

J. Riou (Jussieu)

K. Sato (Nagoya University)

T. Terasoma (University of Tokyo)

N. Yagita (Ibaraki University)

G. Yamashita (RIMS)

T. Yasuda (RIMS)

This workshop is supported by JSPS Core-to-Core Program "New Developments of Arithmetic Geometry, Motive, Galois Theory, and Their Practical Applications" (Coordinator Makoto Matsumoto) and JSPS (B)#17340008 "数論的多様体の$p$進的手法による研究" (representative Nobuo Tsuzuki).

Schedule:

25(Mon)/Sept

10:00-11:00 G. Yamashita (RIMS) Review and Overview.

11:15-12:15 K. Sato (Nagoya Univ.) Motivic cohomology groups with finite coefficients 1.

13:30-14:30 Y. Hashimoto (Osaka City Univ.) Introduction to algebraic topology 1--Eilenberg-MacLane space, Steenrod algebra, Adams spectral sequence.

14:45-15:45 M. Asakura (Kyushu Univ.) Introduction to regulator.

16:00-17:00 A. Pal (IHES) The torsion of Drinfeld modules of rank two.

26(Tue)/Sept

10:00-11:00 K. Sato (Nagoya Univ.) Motivic cohomology groups with finite coefficients 2.

11:15-12:15 S. Mochizuki (Univ. of Tokyo) Reading Morel-Voevodsky 1.

13:30-14:30 Y. Hashimoto (Osaka City Univ.) Introduction to algebraic topology 2--generalized cohomology, spectrum, infinite loop space.

14:45-15:45 N. Minami (Nagoya Institute of Tech.) Symmetric Spectra (following Hovey-Shipley-Smith).

16:00-17:00 J. Riou (Jussieu) Spanier-Whitehead duality in algebraic geometry.

27(Wed)/Sept

10:00-11:00 S. Mochizuki (Univ. of Tokyo) Reading Morel-Voevodsky 2.

11:15-12:15 G. Yamashita (RIMS) Reduced Power Operations 1.

13:30-14:30 N. Yagita (Ibaraki Univ.) Milnor's primitive operations Q_i.

14:45-15:45 T. Yasuda (RIMS) motivic integrals and homological McKay correspondences.

16:00-17:00 J. Riou (Jussieu) Operation on algebraic K-theory and regulators via the homotopy theory of schemes.

Party

28(Thu)/Sept

10:00-11:00 G. Yamashita (RIMS) Reduced Power Operations 2.

11:15-12:15 K. Hagihara (Univ. of Tokyo) related topics of Milnor-Bloch-Kato conjecture.

13:30-14:30 A. Ikeda (Osaka Univ.) Algebraic cycles and differential forms.

14:45-15:45 S. Kimura (Hiroshima Univ.) Introduction to finite dimensional motives.

16:00-17:00 K. Kimura (Tsukuba Univ.) Nori's category of motives.

29(Fri)/Sept

10:00-11:00 K. Hagihara (Univ.of Tokyo) proof of Milnor conjecture (1).

11:15-12:15 K. Hagihara (Univ.of Tokyo) proof of Milnor conjecture (2).

13:30-14:30 K. Kurano (Meiji Univ.) About the algebraic description of intersection multiplicity due to Serre.

14:45-15:45 T. Terasoma (Univ. of Tokyo) Bar construction and its application.

In the morning session of this workshop, K. Hagihara, S. Mochizuki, K. Sato, and G. Yamashita give series lectures on Voevodsky's proof of the Milnor conjecture. In the afternoon session, experts in their areas give introductory talks for beginners. Joe"l Riou's two talks are research talks, but the half of each talk is introductory for beginners. And, Y. Hasimoto, and N. Minami give talks of introduction to homotopy theory for the theory of motives in the view of the algebraic topology. Everyone is welcome.