TL;DR
This paper develops an analog of Leray theory for singular varieties using Whitney stratifications and applies it to provide a clear geometric proof of Parshin's Reciprocity Law for residues.
Contribution
It introduces a new Leray-type framework for singular varieties and applies it to give a transparent proof of Parshin's Residues reciprocity law.
Findings
Established an analog of Leray theory for singular varieties
Provided a geometric proof of Parshin's Reciprocity Law
Connected stratification theory with residue calculus
Abstract
The article consist of two main parts: an analog of the Leray Theory for Singular Varieties and its application to the Theory of Parshin's Residues. The first part is independent from the second. It uses the theory of Whitney stratifications. The second part is an application of the first. In particular, a geometric and very transparent proof of the Parshin's Reciprocity Law for residues is given.
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