Riemann hypothesis for varieties over finite fields
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
gptkb:algebraic_geometry
number theory |
| gptkbp:concerns |
algebraic varieties
finite fields |
| gptkbp:formedBy |
gptkb:André_Weil
1949 |
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann hypothesis for varieties over finite fields
|
| gptkbp:implies |
functional equation for zeta functions
rationality of zeta functions Betti numbers as degrees of polynomials in zeta function |
| gptkbp:partOf |
gptkb:Weil_conjectures
|
| gptkbp:provenBy |
gptkb:Pierre_Deligne
|
| gptkbp:provenUsing |
gptkb:étale_cohomology
gptkb:Grothendieck's_theory |
| gptkbp:relatedTo |
gptkb:Riemann_hypothesis
gptkb:Weil_conjectures |
| gptkbp:state |
the zeros of the zeta function of a non-singular projective variety over a finite field have a specific real part
|
| gptkbp:yearProved |
1974
|
| gptkbp:bfsParent |
gptkb:Weil_zeta_function
|
| gptkbp:bfsLayer |
6
|