| 研究概要 |
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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