International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2005 / Article

Open Access

Volume 2005 |Article ID 147035 | https://doi.org/10.1155/IJMMS.2005.2133

Michael Berg, "Derived categories and the analytic approach to general reciprocity laws. Part I", International Journal of Mathematics and Mathematical Sciences, vol. 2005, Article ID 147035, 26 pages, 2005. https://doi.org/10.1155/IJMMS.2005.2133

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

Received21 Dec 2004

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.

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.


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