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I'm just finished my learning of algebraic number theory, and I want to go for some algebraic geometry which I basically know nothing about. At the same time, I'm informed that there're lots of analogues between number fields and function fields which relates closely to algebraic curves (I guess). So, is there any books that study function fields in certain depth (so we can get some analogues of cohomology groups, Adeles, Ideles, Riemann-Roch, etc) and include basic algebraic geometry? Thanks for advising.

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    $\begingroup$ "Algebraic Function Fields and Codes" by Henning Stichtenoth. $\endgroup$
    – Hanno
    Commented Apr 14, 2020 at 6:20

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Plane algebraic curves by Fischer

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