RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

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

On residues in algebraic geometry

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)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1982, 19:3, 495–520

Bibliographic databases:

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

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} 

• http://mi.mathnet.ru/eng/izv1714
• http://mi.mathnet.ru/eng/izv/v45/i6/p1258

 SHARE:

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
2. I-Chiau Huang, “An Explicit Construction of Residual Complexes”, Journal of Algebra, 225:2 (2000), 698
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
•  Number of views: This page: 238 Full text: 94 References: 30 First page: 1