Derived Categories and the Analytic Approach to General Reciprocity Laws. Part I

Citation data:

International Journal of Mathematics and Mathematical Sciences

Publication Year:
2005
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Repository URL:
https://digitalcommons.lmu.edu/math_fac/45
Author(s):
Berg, Michael
Tags:
Geometry and Topology; Mathematics
article description
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.