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We reformulate Hecke's open problem of 1923, regarding theFourier-analytic proof of higher reciprocity laws, as a theoremabout morphisms involving stratified topological spaces. Weachieve this by placing Kubota's formulations of n-Hilbertreciprocity in a new topological context, suited to theintroduction of derived categories of sheaf complexes.Subsequently, we begin to investigate conditions on associatedsheaves and a derived category of sheaf complexes specificallydesigned for an attack on Hecke's eighty-year-old challenge

Derived categories and the analytic approach to general reciprocity laws. Part I