All Questions

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 (...

My question basically is very simple: when did mathematicians start to do algebraic geometry "outside the complex numbers" ? In the old days, algebraic geometry was solely done over the ...

It is known that there are only finitely many isomorphism classes of abelian variety over a finite field. I am curious about the exact number of these isomorphism classes. Explicitly, fix $g$, let $\...

[Edit] Let me make question more focused. It is about details of Weil conjectures. Rationality of zeta function does NOT require the manifold to be smooth & projective, so zeta function is a ...

To establish the Weil conjectures for $n$-dimensional projective space over a finite field is elementary. Does there exist a simple direct proof of the conjectures for finite field Grassmannians?