A new approach to Grothendieck's variational Hodge conjecture
| Project/Area Number |
17K18723
|
|---|
| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra, Geometry, and related fields
|
|---|
| Research Institution | The University of Tokyo (2018-2019)
Tokyo Institute of Technology (2017) |
|---|
Principal Investigator |
Saito Shuji 東京大学, 大学院数理科学研究科, 教授 (50153804)
|
|---|
| Project Period (FY) |
2017-06-30 – 2020-03-31
|
| Project Status |
Completed (Fiscal Year 2019)
|
| Budget Amount *help |
¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000)
Fiscal Year 2018: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
|
|---|
| Keywords | K理論 / リジッド解析空間 / リジッド解析 / ホッジ予想 / リジッド解析幾何 / モチーフ理論 |
|---|
| Outline of Final Research Achievements |
Hodge conjecture is one of the most important open problems in mathematics. It implies Grothendieck's variational Hodge conjecture while they are equivalent for abelian varieties. By a recent development, the latter conjecture is reduced to the so-called the algebrization problem of algebraic K-theory of formal schemes. This is a vast generalization of Grothendieck's formal existence theorem and is wide open. In our research program, we propose a completely new approach to this problem by introducing a new K-theory for rigid analytic spaces, which brings about possibilities to apply the rigid analytic geometry to the algebrization problem.
|
| Academic Significance and Societal Importance of the Research Achievements |
ホッジ予想が数学の最重要問題のひとつであることに異論はない．クレイ研究所がミレニアム問題の一つとして100万米ドルの懸賞金をかけたこともその理由の一つである．変動的ホッジ予想は，ホッジ予想よりは弱い予想であるが，これに対する新たな結果はホッヂ予想に対する重要な進展をもたらすことが期待される．最近の進展によりこの問題は，形式的スキームの代数的K群にたいする代数化の問題に帰着されたが．これについての一般的アプローチは知られていない．本研究の意義は,リジッド解析空間のK理論を構築することにより, リジッド解析的手法をこの難問に適用するという全く新しいアイデアにもとずくアプローチを与えたことにある．
|
Report
(4 results)
Research Products
(36 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] Theory of motives with modulus2019
Author(s)
Shuji Saito
Organizer
Arithmetic and Algebraic Geometry 2019 on the occasion of Prof. Terasoma's 60-th birthdUniversity of Tokyo, Tokyo Japanay,
Related Report
Int'l Joint Research / Invited
-
[Presentation] Rigid analytic K-theory2018
Author(s)
Shuji Saito
Organizer
Arithmetic and Analysis, Conference on the occasion of Christopher Deninger's 60th birthday
Related Report
Int'l Joint Research / Invited
-
-
-
-
-
-
-
-
-
-
-
-
-
-
