 

Matthew Morrow
An explicit approach to residues on and dualizing sheaves of arithmetic surfaces view print


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


Abstract
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.


Acknowledgements
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
mmorrow@math.uchicago.edu
http://math.uchicago.edu/~mmorrow/

