International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 731093, 19 pages
Research Article

Derived Categories and the Analytic Approach to General Reciprocity Laws: Part III

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

Received 19 October 2009; Revised 3 May 2010; Accepted 12 May 2010

Academic Editor: Pentti Haukkanen

Copyright © 2010 Michael C. 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.


Building on the scaffolding constructed in the first two articles in this series, we now proceed to the geometric phase of our sheaf (-complex) theoretic quasidualization of Kubota's formalism for n-Hilbert reciprocity. Employing recent work by Bridgeland on stability conditions, we extend our yoga of t-structures situated above diagrams of specifically designed derived categories to arrangements of metric spaces or complex manifolds. This prepares the way for proving n-Hilbert reciprocity by means of singularity analysis.