Derived categories and the analytic approach to general reciprocity laws. Part I
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...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2133 |
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| _version_ | 1832555329397719040 |
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| author | Michael Berg |
| author_facet | Michael Berg |
| author_sort | Michael Berg |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-155b6592b83f465686e6ad74572e63a5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-155b6592b83f465686e6ad74572e63a52025-02-03T05:48:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005132133215810.1155/IJMMS.2005.2133Derived categories and the analytic approach to general reciprocity laws. Part IMichael Berg0Department of Mathematics, Loyola Marymount University, Los Angeles 90045, CA, USAWe 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.http://dx.doi.org/10.1155/IJMMS.2005.2133 |
| spellingShingle | Michael Berg Derived categories and the analytic approach to general reciprocity laws. Part I International Journal of Mathematics and Mathematical Sciences |
| title | Derived categories and the analytic approach to general
reciprocity laws. Part I |
| title_full | Derived categories and the analytic approach to general
reciprocity laws. Part I |
| title_fullStr | Derived categories and the analytic approach to general
reciprocity laws. Part I |
| title_full_unstemmed | Derived categories and the analytic approach to general
reciprocity laws. Part I |
| title_short | Derived categories and the analytic approach to general
reciprocity laws. Part I |
| title_sort | derived categories and the analytic approach to general reciprocity laws part i |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2133 |
| work_keys_str_mv | AT michaelberg derivedcategoriesandtheanalyticapproachtogeneralreciprocitylawsparti |