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My question is of historical nature: when did mathematicians start studying algebraic geometry over finite fields in a systematic way, and who were the main driving forces ?

Did it start with Weil (and the Weil conjectures) ?

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  • $\begingroup$ Depends on what exactly you mean by "algebraic geometry" and "systemic". I think a case can be made for Gauss (and his famous "last entry" that motivated the Weil conjectures). $\endgroup$
    – Asvin
    Commented May 10, 2023 at 13:56
  • $\begingroup$ Prior to Weil there were Artin, Schmidt and others, although their study was mostly restricted to curves. See Peter Roquette's informative papers linked to in this relevant MO thread: mathoverflow.net/questions/14627/… $\endgroup$
    – Ofir Gorodetsky
    Commented May 10, 2023 at 13:58

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