2008 Fiscal Year Self-evaluation Report
Stability, Global Galois Representations and Non-Abelian Zeta Functions
| Project/Area Number |
18340012
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
WENG Lin Kyushu University, 大学院・数理学研究院, 准教授 (60304002)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 非可換L-関数 / Eisenstein 級数 / Galois 表現 / 安定性 / リーマン予想 |
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| Research Abstract |
This is a part of our researches on what we call Geometric Arithmetic. This consists of three main parts, namely, one for non-abelian class field theory, CFT for short, one for non-abelian zeta functions and one for geo-arithmetical intersection and cohomology, and the Rimann Hypothesis. In more details, in the part of CFT, we are going to see how our works on a general CFT for function fields over complex numbers, using the natural correspondence between irreducible unitary representations of fundamental groups of punctured Riemann surfaces and stable parabolic bundles of parabolic degree zero, can be worked out for other type of fields, particular for p-adic number fields and algebraic number fields; in the part of non-abelain zeta functions, we are going to introduce genuine non-abelain zetas for global fields using moduli spaces of stable objects and study their properties. As for the final parts about the Riemann hypothesis, we are going to investigate not only the classical RH but that for new zetas we introduced.
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