Derived Categories and the Analytic Approach to General Reciprocity Laws: Part III

Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf (-complex) theoretic quasidualization of Kubota's formalism for n-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga of t-structuressituated above diagrams of specifically designed derived categories to arrangements of metric spaces or complex manifolds. This prepares the way for provingn-Hilbert reciprocity by means of singularity analysis