Grothendieck's trace map for arithmetic surfaces via residues and higher adeles

We establish the reciprocity law along a vertical curve for residues of differential forms on arithmetic surfaces, and describe Grothendieck's trace map of the surface as a sum of residues. Points at infinity are then incorporated into the theory and the reciprocity law is extended to all curve...

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Bibliographic Details
Main Author Morrow, Matthew
Format Journal Article
LanguageEnglish
Published 10.01.2011
Subjects
Mathematics - Algebraic Geometry
Mathematics - Number Theory
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Summary:We establish the reciprocity law along a vertical curve for residues of differential forms on arithmetic surfaces, and describe Grothendieck's trace map of the surface as a sum of residues. Points at infinity are then incorporated into the theory and the reciprocity law is extended to all curves on the surface. Applications to adelic duality for the arithmetic surface are discussed.
DOI:10.48550/arxiv.1101.1883