I recently came across the Hasse-Weil boundary while studying number theory, but I know almost nothing about algebraic geometry, so I don't think I fully understood it.

Does this statement have the same meaning as the Hasse-Weil border?

: For an integer coefficient polynomial $ P (x, y) $, the number of solutions $ N $ to the $ P (x, y) = 0 $ in the $ mathbb {F} _p $ satisfied $ | N-q | le 2g sqrt q $

(I don't know what a genus is; I just saw it as constantly irrelevant $ p $ )