Class Field Theory

  • Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 117)


Let k be a finite field with q = pn elements and let V be an algebraic variety defined over k (or, as one also says, a k-variety). Suppose that V is defined by charts Ui (isomorphic to affine k-varieties) and changes of coordinates uij (with coefficients in k). If x = (x1, …, xr) is a point of an affine space, we write Fx, or xq, for the point with coordinates (xq1, …, xqr). The map xFx commutes with polynomial maps with coefficients in k. In particular, it maps each of the Ui, into itself and commutes with the Uij; therefore by “glueing” it operates on V. The image of a point xV will again be denoted Fx or xq.


Exact Sequence Homogeneous Space Algebraic Group Galois Group Finite Index 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Collège de FranceParis Cedex 05France

Personalised recommendations