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6
votes
Are degrees of polynomials in Weil's zeta function equal/bounded to/by dimensions of SOME co...
The number of points always has an interpretation as a supertrace of Frobenius on the compactly supported cohomology, by the Grothendieck trace formula. The issue is that it can be quite difficult to …
11
votes
Weil Conjectures for Grassmannians
Yes. Both cohomology and number of points are readily determined by looking at the Schubert cells (a cell of dimension k contributes one dimension to $H^{2k}$, and $q^k$ to the point count) and they …
5
votes
Equivalent statements of the Riemann hypothesis in the Weil conjectures
I believe a consequence of the Riemann hypothesis in terms of number of points is that an n-dimensional smooth projective variety X will have $q^n+O(q^{n-1/2})$ points over $\mathbb{F}_q$, and the con …