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arXiv · 0911.0590

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

Matthew Morrow
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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.

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Matthew Morrow. 2009-11-03. An explicit approach to residues on and dualizing sheaves of arithmetic surfaces. https://arxiv.org/abs/0911.0590

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