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

作者：Morrow Matthew^*

来源：The New York Journal of Mathematics, 2010, 16: 575-627.

• Residues
• Reciprocity laws
• Arithmetic surfaces
• Grothendieck duality

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.

• 出版日期2010