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I am reading Serre's "Local Fields". I would like to find more exercises to complement my study. So I am looking for, mabye, exercises from a course that followed this book.

Do you know of such a course with exercises available online? Do you know about some exercises which correspond to the very first chapter (which treats Dedekind domains from the local point of view)? Do you have any suggestions regarding learning from this book, or learning local class field theory in general?

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    $\begingroup$ Lecture notes by Milne are in my experience quite good for self studies or study groups. I don't know if they go well together with Serre's book, though. $\endgroup$ Commented Jul 2, 2013 at 19:21
  • $\begingroup$ Thanks. my original plan was to read Milne's notes, and I will probably read them next. $\endgroup$
    – edo arad
    Commented Jul 3, 2013 at 5:18

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About learning local class-field theory in general, I recommend the book Class Field Theory by Jürgen Neukirch.
It starts from an abstract version of the theory, proceeding to the local theory, and then approaching the global theory both from the adelic method, and from the classical view-point, i.e. ray-class fields. Hope this helps.

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  • $\begingroup$ Thank you! I still haven't given up on Serre, but I will look into it. $\endgroup$
    – edo arad
    Commented Jul 2, 2013 at 18:32
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    $\begingroup$ For anyone interested, there is also "the Bonn lectures", which are a set of notes from CFT lectures by Neukirch. These notes treat CFT from a cohomological approach, unlike the above book. $\endgroup$
    – edo arad
    Commented Jul 3, 2013 at 5:23
  • $\begingroup$ @edoarad Thanks for providing this information. But I cannot tell what the lectures you are referring to. Might you give a reference? And thanks for the editing. $\endgroup$
    – awllower
    Commented Jul 3, 2013 at 7:17
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    $\begingroup$ it can be found in amazon $\endgroup$
    – edo arad
    Commented Jul 3, 2013 at 7:19
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I have found the book Local Fields and Their Extensions which seems to correspond to the start of serre's book with many exercises. There is also the online notes by Stevenhagen, which have a lot of exercises.

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