Re: field and Galois theory

[BORCEUX Francis <borceux@agel.ucl.ac.be>]

As possible answer to the following message of Tobias Schroeder to this list

>all introductions to field and Galois theory I've found are written in a
>"classical" way, i.e. making not much use of categorical notions. A lot of
>computation is done where someone who is "categorical minded" has the
>feeling that the results could be established in a more comprehensible and
>clear way by category theory. -- Does somebody have a reference to a short
>and good introduction to field and Galois theory from a categorical
>viewpoint?

let me mention the book

   Galois theories
   Francis Borceux & George Janelidze
   Cambridge Studies in Advanced Mathematics, volume 72
   Cambridge University Press (2001), 341 pages
   ISBN 0 521 80309 8 

which will be available from February 20.

This is probably not an as "short" introduction as Tobias wants ... 
and I let you decide if it is a "good" one.

References at the end of the book, in particular to various papers of
George Janelidze on a categorical approach of Galois theory, will provide
alternative answers to Tobias'question.

Here is the table of contents of the book.

   1. Classical Galois theory
   2. Galois theory of Grothendieck
   3. Infinitary Galois theory
   4. Categorical Galois theory of commutative rings
   5. Categorical Galois theorem and factorization systems
   6. Covering maps
   7. Non-galoisian Galois theory

For further information, contact

   WWW: http://www.cambridge.org


Francis Borceux
   

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