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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 13, Pages 2133-2158

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

Department of Mathematics, Loyola Marymount University, Los Angeles 90045, CA, USA

Received 21 December 2004

Copyright © 2005 Michael Berg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.