| Budget Amount *help |
¥18,200,000 (Direct Cost: ¥14,000,000、Indirect Cost: ¥4,200,000)
Fiscal Year 2014: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
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| Outline of Final Research Achievements |
As a tool to study vector bundles on algebraic varieties, we have the notion of Chern class, which measures `how a vector bundle is twisted', in a linear space called cohomology. In this research under report, we start with a naive quiestion concernning `in what kind of cohomology the Chern classes are defined', and formulated a minimal set of axioms for such cohomology. We also proved the Riemann-Roch theorem holds in such cohomology theories.
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