In mathematics, specifically arithmetic geometry, prismatic cohomology is a cohomology introduced by Bhargav Bhatt and Peter Scholze for -adic formal schemes. It generalizes various -adic cohomology theories.
Fix a prime . A prism is a pair , where is a -ring with -derivation and is an ideal of defining a Cartier divisor in , such that is derived -adically complete and the ideal contains , where the associated map given by is a ring homomorphism, which then necessarily lifts the Frobenius endomorphism on .
See also Crystalline cohomology Motivic cohomology de Rham cohomology
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