Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I've read numerous introductions to finite fields, but I feel like my intuition about them is fairly lacking. Considering that finite fields are the the most "inert" objects in algebraic geometry, I think I could use a serious surge of perspective.

What I would like to read now is a comprehensive overview that tells me "everything I need to know" about how finite fields and their algebraic closures work, algebraically. I don't mind working out the proofs on my own if they are terse or absent; I'm just looking for quality and quantity of results. Hopefully some intense reading will help steep out some of my insecurities about characteristic p.

Can anyone recommend a single source for such an overview?

Thanks!

share|improve this question
    
If you are a geometer over finite fields, then the Frobenius will make sure that you are almost as good as in the algebraically closed case. Befriend the Frobenius, and then you are in a safe position. –  Regenbogen Feb 26 '10 at 0:15
add comment

2 Answers

up vote 9 down vote accepted

Finite Fields by R. Lidl and H Niederreiter (CUP). Probably as comprehensive as it gets.
The ams review calls it the ``the Bible of finite fields''. You can find it (the review)here.

share|improve this answer
1  
Your link appears to be broken. –  Alison Miller Oct 24 '09 at 0:37
    
Fixed it now. Thanks! –  Sonia Balagopalan Oct 24 '09 at 0:58
    
It's great, thank-you! –  Andrew Critch Oct 24 '09 at 5:49
add comment

The really important things in algebraic number theory start from group cohomology and theorems like Hilbert 90, but you'll be better searching/asking for different keywords than finite fields then.

share|improve this answer
    
What I'm looking for is a single comprehensive source (just edited the question to reflect this). –  Andrew Critch Oct 23 '09 at 23:25
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.