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

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

2009-11-03

arxiv.org/abs/0911.0590v2

New York Journal of Mathematics, vol. 16, 2010, pp. 575 -- 627, http://nyjm.albany.edu/j/2010/16-25.html

Mathematics

Number Theory

This is an update and correction to an earlier version of the paper, entitled "An explicit approach to residues on and canonic

Scientific paper

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.

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