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Let $X\hookrightarrow\mathbb{P}^n_{\mathbb{F}_q}$ be a pure dimensional projective scheme of dimension $d$. So we know a trivial estimate of the number of $X(\mathbb F_q)$ is that $\#X(\mathbb F_q)\leqslant\deg(X)(q^d+\cdots+1)$.

I want to know where I can find a reference of the proof of this result. Only requirement is that it must be a "published" reference.

Thank you.

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  • $\begingroup$ The argument that leads to that upper bound is, essentially, contained in p. 236 of Barry Mazur's Arcata contribution, "Eigenvalues of Frobenius acting on algebraic varieties over finite fields." $\endgroup$
    – Jason Starr
    Commented Mar 19, 2016 at 16:10
  • $\begingroup$ That's exactly what I want, thank you very much, Prof. Starr. $\endgroup$
    – var
    Commented Mar 19, 2016 at 16:37

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