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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 6, Pages 1258–1287 (Mi izv1714)  

This article is cited in 3 scientific papers (total in 3 papers)

On residues in algebraic geometry

V. G. Lomadze


Abstract: Let $f\colon X\to S$ be a dominant morphism of algebraic schemes, with $S$ integral. Let $n$ be the relative dimension of $f$ and let $x=(x_0,x_1,…,x_n)$ be a sequence of points of $X$ such that, for all $0\leqslant i\leqslant n$, $x_i$ is a specialization of $x_{i-1}$, has codimension $i$ and is mapped into the generic point of $S$. Under these conditions a residue mapping (of $f$ into the “chain” $x$)
$$ \operatorname{Res}_x^f\colon\Omega^*(X)\to\Omega^*(S) $$
is defined and its main properties, in particular the “residue formula”, are proved.
Bibliography: 14 titles.

Full text: PDF file (2684 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:3, 495–520

Bibliographic databases:

UDC: 513.6
MSC: Primary 14A15; Secondary 13J10, 13H99, 14B05
Received: 04.12.1980

Citation: V. G. Lomadze, “On residues in algebraic geometry”, Izv. Akad. Nauk SSSR Ser. Mat., 45:6 (1981), 1258–1287; Math. USSR-Izv., 19:3 (1982), 495–520

Citation in format AMSBIB
\Bibitem{Lom81}
\by V.~G.~Lomadze
\paper On~residues in algebraic geometry
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 6
\pages 1258--1287
\mathnet{http://mi.mathnet.ru/izv1714}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=641802}
\zmath{https://zbmath.org/?q=an:0528.14003}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 3
\pages 495--520
\crossref{https://doi.org/10.1070/IM1982v019n03ABEH001426}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zhongming Tang, “An algebraic approach to the residues in algebraic geometry”, Math Z, 203:1 (1990), 1  crossref  mathscinet  zmath  isi
    2. I-Chiau Huang, “An Explicit Construction of Residual Complexes”, Journal of Algebra, 225:2 (2000), 698  crossref
    3. Sergey O. Gorchinskiy, Denis V. Osipov, “Continuous homomorphisms between algebras of iterated Laurent series over a ring”, Proc. Steklov Inst. Math., 294 (2016), 47–66  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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