| Budget Amount *help |
¥15,730,000 (Direct Cost: ¥12,100,000、Indirect Cost: ¥3,630,000)
Fiscal Year 2014: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2010: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
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| Outline of Final Research Achievements |
The research consists of three parts:(I) Higher dimensional class field theory, (II) Cohomological Hasse principle, (III) Finiteness of motivic cohomology.
(I) We generalized higher dimensional class field theory of Kato-Saito by using Chow groups of zero-cycles with modulus and gives a proof of the rank-one case of a conjecture of Deligne-Drinfeld on the existence of smooth l-adic sheaves on varieties over finite fields. (II)We proved rthe prime-to-p part of the Kato conjecture on cohomological Hasse principle and gives several applications on various problems in arithmetic geometry; special values of zeta functions, and a generalization of higher dimensional class field theory in the framework of theory of motivic cohomology, and a geometric application to resolution of singularities. (III) We gave new contributions to the finiteness conjecture of motivic (co)homology of arithmetic schemes. It shows the finiteness of motivic (co)homology with finite coefficient of arithmetic schemes.
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