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Basic Number Theory

Andre Weil
Publisher: 
Springer Verlag
Publication Date: 
1995
Number of Pages: 
315
Format: 
Paperback
Edition: 
3
Series: 
Classics in Mathematics
Price: 
49.95
ISBN: 
3540586555
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on
07/16/2009
]

This is definitely a classic, but it is hardly “Basic.” The very first section includes a proof that there are no finite skew-fields, and the second famously begins by defining the p-adic absolute values in terms of the additive Haar measure on a locally compact topological field.

That out of the way, Weil’s classic exposition of local and global class field theory should certainly be on every young number theorist’s reading list.


 

 Elementary Theory: Locally compact fields.- Lattices and duality over local fields.- Places of A-fields.- Adeles.- Algebraic number fields.- The theorem of Riemann-Roch.- Zeta-functions of A-fields.- Traces and norms.- Classfield Theory: Simple algebras.- Simple algebras over local fields.- Simple algebras over A-fields.- Local classfield theory.- Global classfield theory.

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