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Residues of regular and meromorphic differential forms. (English) Zbl 0814.14022
For varieties over perfect fields residues of differential forms can be constructed both cohomologically and using higher dimensional local fields. Related to the two types of residues are two constructions of residual complexes. We will exhibit an explicit isomorphism between the two constructions, thus obtaining also a relation between the two types of residues and the integrals derived from them. Using this we can compare various results of the different residue theories, and we can combine them to prove a generalization of a theorem of Newton on the centroids of the intersection schemes of two plane curves.

##### MSC:
 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 13N10 Commutative rings of differential operators and their modules 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 32A27 Residues for several complex variables
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