Derived categories and the analytic approach to generalreciprocity laws. Part I | Zendy

Michael C. Berg | Zendy

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Derived categories and the analytic approach to generalreciprocity laws. Part I

Author(s) -

Michael C. Berg

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.2133

Subject(s) - mathematics , morphism , reciprocity law , sheaf , context (archaeology) , reciprocity (cultural anthropology) , pure mathematics , topological space , algebra over a field , psychology , social psychology , paleontology , biology

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

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