Statements (55)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:cohomology_theory
|
| gptkbp:appliesTo |
schemes
|
| gptkbp:enables |
study of Galois representations
study of L-functions study of étale cohomology with coefficients in l-adic sheaves study of étale cohomology with coefficients in torsion sheaves study of étale cohomology with coefficients in Z/lZ comparison theorems with classical cohomology definition of Chern classes in algebraic geometry definition of cycle class maps definition of fundamental group of a scheme study of Artin–Schreier sequence study of Brauer group study of Kummer sequence study of Lefschetz theorems study of Picard group study of Poincaré duality study of constructible sheaves study of duality theorems study of intersection theory study of local systems study of perverse sheaves study of purity theorems study of rational points on varieties study of sheaf cohomology study of smooth and proper base change theorems study of torsion phenomena in algebraic geometry study of zeta functions of varieties study of étale cohomology with compact support study of étale fundamental group study of étale sheaves study of étale cohomology with coefficients in finite abelian groups study of étale cohomology with coefficients in Q_l |
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:firstAppearance |
1960s
|
| gptkbp:generalizes |
singular cohomology
|
| gptkbp:hasApplication |
gptkb:topology
number theory arithmetic geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
étale cohomology
|
| gptkbp:introduced |
gptkb:Alexander_Grothendieck
|
| gptkbp:provides |
cohomological invariants
|
| gptkbp:relatedTo |
gptkb:Galois_cohomology
gptkb:l-adic_cohomology motivic cohomology |
| gptkbp:usedFor |
gptkb:proving_Weil_conjectures
studying algebraic varieties |
| gptkbp:uses |
gptkb:étale_topology
|
| gptkbp:bfsParent |
gptkb:algebraic_geometry
gptkb:Algebraic_geometry gptkb:Tate_conjecture gptkb:Weil_conjectures gptkb:Tate_module gptkb:Alexander_Grothendieck |
| gptkbp:bfsLayer |
5
|