| Budget Amount *help |
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Research Abstract |
By a joint work with Shinichi Mochizuki, we proved the injectivity portion of the combinatorial cuspidalization; moreover, as an arithmetic application of this injectivity, we obtained the faithfulness of the outer Galois representations associated to hyperbolic curves over number or p-adic local fields. Next, I introduced the notion of monodromic fullness for hyperbolic curves and proved an anabelian conjecture-type result for certain monodromically full hyperbolic curves of genus zero. Finally, I proved that in general, the pro-p section conjecture for hyperbolic curves over number fields, as well as p-adic local fields, cannot be resolved in the affirmative.
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