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 -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.