New York Journal of Mathematics
Volume 16 (2010) 575-627


Matthew Morrow

An explicit approach to residues on and dualizing sheaves of arithmetic surfaces

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Published: December 5, 2010
Keywords: Residues; Reciprocity laws; Arithmetic surfaces; Grothendieck duality
Subject: 14H25 (Primary), 14B15 14F10 (Secondary)

We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for surfaces over a perfect field. In an appendix, explicit local ramification theory is used to recover the fact that in the case of a local complete intersection the dualizing and canonical sheaves coincide.


Much of the work in this paper was done while I was the recipient of the Cecil King Travel prize, through the London Mathematical Society; I would like to thank the Cecil King Foundation for their generosity.

Author information

Department of Mathematics, University of Chicago, Chicago, IL 60637