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

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.

This is an update and correction to an earlier version of the paper, entitled "An explicit approach to residues on and canonical sheaves of arithmetic surfaces"; an erroneous lemma (lemma 5.4) in the earlier version necessitated restructuring of the paper, though the main results are largely unchanged

References in corpus (2)

• Fubini's theorem and non-linear change of variables over a two-dimensional local field
• On ramification filtrations and $p$-adic differential modules, I: equal characteristic case

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• Two-Dimensional Local-Global Class Field Theory in Positive Characteristic
• LCA(2), Weil index, and product formula
• Reciprocity Laws for the Higher Tame Symbol and the Witt Symbol on an Algebraic Surface