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- Q5191431 subject Q13252973.
- Q5191431 subject Q8234760.
- Q5191431 subject Q8521232.
- Q5191431 abstract "In mathematics, crystalline cohomology is a Weil cohomology theory for schemes introduced by Alexander Grothendieck (1966, 1968) and developed by Pierre Berthelot (1974). Its values are modules over rings of Witt vectors over the base field. Crystalline cohomology is partly inspired by the p-adic proof in Dwork (1960) of part of the Weil conjectures and is closely related to the algebraic version of de Rham cohomology that was introduced by Grothendieck (1963). Roughly speaking, crystalline cohomology of a variety X in characteristic p is the de Rham cohomology of a smooth lift of X to characteristic 0, while de Rham cohomology of X is the crystalline cohomology reduced mod p (after taking into account higher Tors).The idea of crystalline cohomology, roughly, is to replace the Zariski open sets of a scheme by infinitesimal thickenings of Zariski open sets with divided power structures. The motivation for this is that it can then be calculated by taking a local lifting of a scheme from characteristic p to characteristic 0 and employing an appropriate version of algebraic de Rham cohomology.Crystalline cohomology only works well for smooth proper schemes. Rigid cohomology extends it to more general schemes.".
- Q5191431 wikiPageExternalLink DixExp.pdf.
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- Q5191431 comment "In mathematics, crystalline cohomology is a Weil cohomology theory for schemes introduced by Alexander Grothendieck (1966, 1968) and developed by Pierre Berthelot (1974). Its values are modules over rings of Witt vectors over the base field. Crystalline cohomology is partly inspired by the p-adic proof in Dwork (1960) of part of the Weil conjectures and is closely related to the algebraic version of de Rham cohomology that was introduced by Grothendieck (1963).".
- Q5191431 label "Crystalline cohomology".