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

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  • Michael Berg

Abstract

We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. We achieve this by placing Kubota's formulations of n -Hilbert reciprocity in a new topological context, suited to the introduction of derived categories of sheaf complexes. Subsequently, we begin to investigate conditions on associated sheaves and a derived category of sheaf complexes specifically designed for an attack on Hecke's eighty-year-old challenge.

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  • Michael Berg, 2005. "Derived categories and the analytic approach to general reciprocity laws. Part I," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-26, January.
    • Handle: RePEc:hin:jijmms:147035
    DOI: 10.1155/IJMMS.2005.2133
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