Advertisement

Rational Equivalence

Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 2)

Summary

A cycle on an arbitrary algebraic variety (or scheme) X is a finite formal sum Σ n V [V] of (irreducible) subvarieties of X, with integer coefficients. A rational function r on any subvariety of X determines a cycle [div(r)]. Cycles differing by a sum of such cycles are defined to be rationally equivalent. Alternatively, rational equivalence is generated by cycles of the form [V(0)] − [V(∞)] for subvarieties V of X × ℙ1 which project dominantly to ℙ1. The group of rational equivalence classes on X is denoted A * X.

Keywords

Exact Sequence Irreducible Component Local Ring Rational Equivalence Abelian Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Personalised recommendations