Let $X$ be an algebraic variety over $\mathbb{F}\_q$ with dimensional $n$. We know that if $X$ is smooth than $X$ has about $q^{nk}$ rational points over $\mathbb{F}\_{q^k}$ (Weil hypothesis). Is there an analogous statement for non-smooth varieties?



Number of rational points in a non-smooth variety
As per Daniel Loughran's comment, I found [this](https://terrytao.wordpress.com/2012/08/31/the-lang-weil-bound/) very nice exposition by Terence Tao which seems to answer the question in detail.


