Statements (49)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:appliesTo |
schemes
algebraic stacks |
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:generalizes |
singular cohomology
|
| gptkbp:hasApplication |
gptkb:l-adic_cohomology
number theory arithmetic geometry motivic cohomology proof of the Weil conjectures |
| gptkbp:hasInvariant |
étale cohomology group
|
| gptkbp:hasProperty |
gptkb:Poincaré_duality
gptkb:Lefschetz_trace_formula gptkb:Mayer–Vietoris_sequence gptkb:Künneth_formula gptkb:finiteness_theorem cycle class map long exact sequence functoriality Galois action base change property comparison theorem comparison with Betti cohomology comparison with de Rham cohomology l-adic coefficients local-to-global spectral sequence proper base change theorem smooth base change theorem supports coefficients in torsion sheaves supports non-algebraically closed fields supports nontrivial Galois modules supports nontrivial fundamental group supports nontrivial sheaf theory supports nontrivial étale covers supports torsion phenomena |
| https://www.w3.org/2000/01/rdf-schema#label |
Étale cohomology
|
| gptkbp:introduced |
gptkb:Alexander_Grothendieck
|
| gptkbp:relatedTo |
gptkb:Galois_cohomology
sheaf cohomology topological cohomology |
| gptkbp:usedFor |
studying algebraic varieties
proving the Weil conjectures |
| gptkbp:uses |
gptkb:étale_topology
gptkb:Čech_cohomology spectral sequence derived functor sheaves |
| gptkbp:bfsParent |
gptkb:Zeta_function_of_a_variety
|
| gptkbp:bfsLayer |
5
|