crystalline cohomology

URI: https://gptkb.org/entity/crystalline_cohomology
GPTKB entity
Statements (23)
Predicate Object
gptkbp:instanceOf gptkb:cohomology_theory
gptkbp:appliesTo schemes over a field of positive characteristic
gptkbp:citation Pierre Berthelot, 'Cohomologie Cristalline des Schémas de Caractéristique p>0', Lecture Notes in Mathematics, Vol. 407, Springer, 1974
gptkbp:coefficientRing gptkb:Witt_vectors
gptkbp:field gptkb:algebraic_geometry
gptkbp:generalizes de Rham cohomology in characteristic zero
gptkbp:hasComparisonTheoremWith gptkb:étale_cohomology_(via_p-adic_Hodge_theory)
gptkb:de_Rham_cohomology_(in_characteristic_zero)
gptkbp:hasFunctoriality yes
https://www.w3.org/2000/01/rdf-schema#label crystalline cohomology
gptkbp:introduced gptkb:Pierre_Berthelot
gptkb:Alexander_Grothendieck
gptkbp:introducedIn 1960s
gptkbp:provides Weil cohomology theory
gptkbp:relatedTo gptkb:étale_cohomology
gptkb:p-adic_cohomology
gptkb:de_Rham_cohomology
gptkbp:studiedIn p-adic Hodge theory
gptkbp:usedFor proving the Weil conjectures
studying algebraic varieties in characteristic p
gptkbp:bfsParent gptkb:Witt_vector
gptkb:Luc_Illusie
gptkbp:bfsLayer 5