I came across the book Basic number theory by André Weil. It mainly introduces concept of Adeles, classification of locally compact fields, adelic points in varieties and schemes in modern number theory. The book however do not contains an explicit problem section. So I would be highly grateful if anyone recommends problem books on this topics in modern number theory. Any help would be appreciated thank you.

  • 3
    $\begingroup$ That book does not discuss adelic points in varieties or schemes: it is about adeles and ideles, $L$-functions, and class field theory. In any case, see the exercises from Ramakrishna and Valenza's book "Fourier Analysis in Number Fields" for exercises on basic topics related to adeles in the direction of Tate's thesis. $\endgroup$
    – KCd
    Jun 20, 2021 at 6:49
  • $\begingroup$ Thank you very much for the reference $\endgroup$ Jun 20, 2021 at 6:54
  • 1
    $\begingroup$ How about Problems in Algebraic Number Theory by Jody Esmonde and M. Ram Murty? $\endgroup$ Jul 1, 2021 at 15:27
  • $\begingroup$ Thanks a lot for the reference $\endgroup$ Jul 1, 2021 at 18:05


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