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Results tagged with weil-conjectures
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user 297
16
votes
Can one find the hodge number by counting points over finite fields?
It is worth mentioning the "Newton above Hodge" theorem. This is a way in which the point count can impose nontrivial conditions on the Hodge numbers, beyond knowing the Betti numbers.
As I assume y …
- 156k
9
votes
Accepted
Could the Weil zeroes of curves be evenly distributed?
If $q$ is a prime for which $2$ is a primitive root, then I claim that the Frobenius eigenvalues of the curve $y^2-y = x^q$ over $\mathbb{F}_2$ have spacing exactly $\tfrac{2 \pi}{q-1}$. This, if Arti …
- 156k
7
votes
Equivalent statements of the Riemann hypothesis in the Weil conjectures
Regarding the question about higher dimensions, Scholl showed that RH in all dimensions follows from the statement:
If $X$ is a smooth hypersurface in $\mathbb{P}^{d+1}$ over $\mathbb{F}_q$, then $X( …
- 156k