| Budget Amount *help |
¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000)
Fiscal Year 2019: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
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)
Fiscal Year 2016: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2015: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
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| Outline of Final Research Achievements |
The research consists of two parts: (I) Generalization of theory of motives. (II) Construction of K-theory for rigid analytic spaces.
(1) We extended Voevodksy's theory of motives. Voevodksy’s theory is based on homotopy invariant sheaves. In order to extend Voevodsky's theory, we introduced reciprocity sheaves as generalization of homotopy invariant sheaves. We proved several basic properties on reciprocity sheaves, which gives a motivic interpretation of some classical theorems on cohomology such as the projective bundle formula and Grothendieck duality. Moreover, we applied theory of reciprocity sheaves to ramification theory.
(2) Motivated by works of Bloch-Esnault-Kerz and Morrow on Grothendieck's variational Hodge conjecture, we constructed a new theory of analytic K-theory of rigid spaces.It sheds new light on Grothendieck's variational Hodge conjecture from the new perspective of rigid analytic geometry.
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