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I am looking for complete references on places, valuations and so on. In particular I need to understand the meaning of "a finite place does not divide a prime number $\ell$" and what is the Frobenius automorphism at a place.

Thank you

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There are countless references that treat the subject of valuations on various classes of fields, in varying degrees of generality. I'm not sure what your criteria for completeness are. J.S. Milne's online notes on algebraic number theory treat valuations of number fields as well as Frobenius elements, and they are fairly introductory (and very nice). Neukirch's Algebraic Number Theory might be close to "complete," although it's perhaps not ideal for an introduction. There are dozens of others. –  Keenan Kidwell Feb 9 '11 at 19:18
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I second the recommendation of Milne's notes. Also, I have found the second half of these notes by William Stein helpful: modular.math.washington.edu/129/ant –  Vitaly Lorman Feb 9 '11 at 19:58
    
Shouldn't this be tagged reference-request? –  awllower Mar 6 '11 at 3:30
    
@awllower ofcourse –  Dinesh Sep 14 '11 at 22:56

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