Crystalline Cohomology RG

In the academic year 2021-2022 we are organising a reading group on the crystalline cohomology of algebraic varieties in positive characteristic. We meet every week on Wednesday at 5pm in MA B1 524 . The (tentative) list of talks is the following:

• 8th December, Fabio Bernasconi: Why crystalline cohomology? Notes

• 15th December, Jefferson Baudin: Serre construction of Witt vector cohomology. Notes

• 23rd February, Maxim Mornev: Isocrystals and Dieudonné-Manin classification.

• 2nd March, Maxim Mornev.: Newton and Hodge polygons. Notes.

• 9th March, Lucas Gerth: p-divisible groups and Dieudonné theory.

• 16th March, Quentin Posva: PD structures.

• 23rd March, Quentin Posva: PD structure II.

• 6th April, Fabio Bernasconi: Crystalline topos. Notes

• 13th April, Jefferson Baudin: Crystals. Notes

• 27th April, Jefferson Baudin: Comparison theorem with de Rham cohomology I. Notes

• May the 4th (be with you): Comparison theorem with de Rham cohomology II

• 11th May, Fabio Bernasconi: Frobenius and Hodge filtration

• 18th May, Fabio Bernasconi: Frobenius and Hodge filtration II

References:

• P. Berthelot and A. Ogus, Notes on Crystalline Cohomology.

• A. Chambert-Loir, Cohomologie cristalline, un survol.

• L. Illusie, Complexe de de Rham-Witt et cohomologie cristalline

• B. Bhatt, A. de Jong, Crystalline cohomology and de Rham cohomology