Introduction to crystalline cohomology

par Livia Grammatica (IRMA)

mercredi 4 nov. 2026, 14:00 → 15:00 Europe/Paris

Pierre Grisvard (IHP)

Arithmetic geometers study problems from number theory using tools inspired by differential geometry or topology. To achieve this they have defined, over the years, many algebraic counterparts to the classical cohomology groups of topology. Crystalline cohomology is one of these counterparts, and it is extremely useful for studying varieties in positive and mixed characteristic. In this talk, we will present its fundamental properties and show how to compute it using the de Rham cohomology of lifts to characteristic 0.