Theme:
The objectives of this workshop are
1. to introduce algebraic K-theory of spaces introduced by Waldhausen and
non-connected K-theory (negative K-theory) of Bass, Thomason-Trobaugh and Schlichting etc. for non-experts.
2. to report recent progress of open problems below in motive theory and algebraic K-theory:
Tate conjecture, Standard conjecture, Hodge conjecture, Beilinson conjecture, Gersten conjecture,
Weibel's K-dimensional conjecture and so on. In particular, we emphasize the logical connection among these conjectures.
Date: June 30 - July 2, 2008
Place: RIMS, Kyoto (Conference room 420)
Access: Getting to the RIMS
Registration: Click here for Registration Form
Speakers:
Roozbeh Hazrat,
Toshiro Hiranouchi,
Yuki Kato,
Shun-ichi Kimura,
Andrea Miller,
Satoshi Mochizuki,
Kanetomo Sato,
Yuichiro Takeda,
Seidai Yasuda
Program
| First day: | ||
| 10:00 - 11:45 | Kanetomo Sato, | What is motive theory? |
| 13:15 - 14:45 | Toshiro Hiranouchi, | Fundamental theorems in Waldhausen K-theory after Schlichting and others |
| 15:00 - 16:30 | Toshiro Hiranouchi, | Non-connected K-theory as a derived invariant |
| 16:45 - 18:05 | Yuichiro Takeda, | K-theoretic reformulation of Tate conjecture over finite fields |
| Second day: | ||
| 10:00 - 11:00 | Roozbeh Hazrat, | Higher K-theory of Azumaya algebras |
| 11:15 - 12:15 | Satoshi Mochizuki, | On Gersten conjecture |
| 13:45 - 14:45 | Yuki Kato, | Higher Chow group and Milnor K-theory of Discrete valuation rings (abstract) |
| 15:00 - 17:00 | Satoshi Mochizuki, | Does Weil conjecture imply Tate conjecture over finite fields? |
| Third day: | ||
| 10:00 - 11:00 | Andrea Miller, | Chow-Kuenneth decompositions for some mixed Shimura varieties (abstract) |
| 11:15 - 12:15 | Shun-ichi Kimura, | Kernel and Cokernel of the cycle map |
| 13:45 - 14:45 | Kanetomo Sato, | Higher cycle class maps for $p$-adic étale Tate twists |
| 15:00 - 17:00 | Seidai Yasuda, | Does Tate conjecture imply the standard conjectures? |
Reference
For higher algebraic K-theory:
D. Quillen, Higher algebraic K-theory I
D. Grayson, Higher algebraic K-theory II after Quillen
F. Waldhausen, Algebraic K-theory of spaces
R. W. Thomason and T. Trobaugh, Higher algebraic K-theory of schemes and derived categories
available at
http://www.math.lsu.edu/~mschlich/K-theory/indexFall08.html.
For non-connected K-theory:
M. Schlichting, Negative K-theory of derived categories, Math. Z. 253 (2006), no. 1, 97--134.
M. Schlichting, Delooping the K-theory of exact categories, Topology 43 (2004) no. 5, 1089-1103.
M. Schlichting, Higher algebraic K-theory (after Quillen, Thomason, and others)
For Thomason descent theory:
R. W. Thomason, algebraic K-theory and etale cohomology,
Annales scientifiques de l'École Normale Supérieure Sér. 4, 18 no. 3 (1985), p. 437-552
S. A. Mitchell, Hypercohomology spectra and Thomason's descent theorem
Organizers
Toshiro Hiranouchi: hiranouchi (at) math.kyushu-u.ac.jp,
Shun-ichi Kimura: kimura (at) math.sci.hiroshima-u.ac.jp,
Satoshi Mochizuki: mochi81 (at) hotmail.com,
Kanetomo Sato: kanetomo (at) math.nagoya-u.ac.jp,
Seidai Yasuda: yasuda (at) kurims.kyoto-u.ac.jp
