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For smooth schemes the category $MF$ (defined by Fontaine for DVR's) realises the "mysterious functor", and provides natural systems of coeffients for crystalline cohomology. We generalise it to schemes with semistable singularities. The new technical features consist mainly of different methods in commutative algebra.
Recording during the thematic meeting: ''Arithmetic geometry, representation theory and applications'' the June 22, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Pascal Vichi Video editing: Guillaume Hennenfent