| Budget Amount *help |
¥19,370,000 (Direct Cost: ¥14,900,000、Indirect Cost: ¥4,470,000)
Fiscal Year 2013: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥6,890,000 (Direct Cost: ¥5,300,000、Indirect Cost: ¥1,590,000)
Fiscal Year 2011: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2010: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
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| Research Abstract |
I find that non-logarithmic version is geometrically more important than the logarithmic one in ramification theory. I constructed the non-logarithmic theory of the characteristic cycle of an l-adic sheaf in codimension at most 1. Using the method of cutting by curves and established acyclicity of morphisms of varieties.
For a sheaf on a surface, I defined the characteristic cycle everywhere on the surface and proved a formula for the Euler number and an analog of the Milnor formula on vanishing cycles. Though limited to surfaces, this is a significant result achieving the aim to construct a theory of characteristic cycles in higher dimension.
I also studied the determinant and the second Stiefel-Whitney class of the Galois representation defined by l-adic cohomology of a variety of even dimension.
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