most recent 30 from http://mathoverflow.net 2013-05-21T21:08:38Z http://mathoverflow.net/feeds/question/2215 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/2215/a-comprehensive-overview-of-finite-fields Andrew Critch 2009-10-23T23:10:49Z 2009-11-12T16:44:45Z

<p>I've read numerous <em>introductions</em> 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.</p> <p>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.</p> <p>Can anyone recommend a single source for such an overview?</p> <p>Thanks!</p>

http://mathoverflow.net/questions/2215/a-comprehensive-overview-of-finite-fields/2216#2216 Ilya Nikokoshev 2009-10-23T23:14:24Z 2009-10-23T23:14:24Z

<p>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 <code>finite fields</code> then.</p>

http://mathoverflow.net/questions/2215/a-comprehensive-overview-of-finite-fields/2223#2223 Sonia Balagopalan 2009-10-23T23:44:43Z 2009-11-09T15:16:41Z

<p><a href="http://books.google.com/books?id=xqMqxQTFUkMC" rel="nofollow">Finite Fields</a> by R. Lidl and H Niederreiter (CUP). Probably as comprehensive as it gets.<br/> The ams review calls it the ``the Bible of finite fields''. You can find it (the review)<a href="http://www.ams.org/bull/1999-36-01/S0273-0979-99-00768-5/S0273-0979-99-00768-5.pdf" rel="nofollow">here</a>.</p>