All Questions

I am currently reading SGA 4$\frac{1}{2}$, exposé 2: Rapport sur la formule des traces. The $L$-series associated to a scheme $X$ of finite type over $\mathbb{F}_{p}$ is defined as $$L(X,s):=\prod_{x\...

If $p$ is a prime, $n\in\mathbb{N}$ is a natural number and $C$ is a nonsingular curve over $\mathbb{F}_{p^{n}}$, the $\zeta$ function associated to $C\mid_{\mathbb{F}_{p^{n}}}$ is defined as \begin{...

Let $X$ be a smooth projective variety over $\mathbb{F}_{q}$. For each pair of positive integers $n$ and $d$, let $\text{Chow}_{n,d}(X)$ denote the (coarse) moduli space of $n$-cycles of degree $d$ on ...

We know that the Riemann zeta function can be generalized to multivariate zeta functions. Is there a multivariate analog of the Weil conjectures?

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?