WiSe 22/23 Oberseminar: Absolute prismatic cohomology
Time and place: Wednesday 16:15-17:45 in M311 and online
Absolute prismatic cohomology is a cohomology theory for p-adic formal schemes developed by Bhatt and Lurie, following the introduction of the prismatic site by Bhatt and Scholze. Roughly speaking, this theory serves as a bridge between the crystalline cohomology of the special fiber and the étale cohomology of the generic fiber. It also leads to a general definition of syntomic cohomology with p-adic coefficients, and ultimately of motivic cohomology with integral coefficients, of arbitrary (derived) schemes.
In this seminar we will learn absolute prismatic cohomology via the (essentially self-contained) article by Bhatt and Lurie:
We will in particular review the definitions of prisms and relative prismatic cohomology and learn about the Cartier–Witt stack, absolute prismatic cohomology, the Nygaard filtration and the syntomic cohomology of formal schemes and of schemes.
| Date | Speaker | Topic |
|---|---|---|
| 26.10 | Marc Hoyois | Introduction and background on prisms |
| 02.11 | Massimo Pippi | Breuil–Kisin twists and the prismatic logarithm |
| 09.11 | Pavel Sechin | The Cartier–Witt stack I |
| 16.11 | Denis Nardin | The Cartier–Witt stack II |
| 23.11 | Suraj Yadav | Review of de Rham complexes and crystalline cohomology |
| 30.11 | Peng Du | Relative prismatic cohomology |
| 07.12 | Marc Hoyois | Absolute prismatic cohomology and Hodge–Tate cohomology |
| 14.12 | Thomas Jacob | Crystalline comparison and the diffracted Hodge complex |
| 21.12 | Marc Hoyois | The Nygaard filtration |
| 11.01 | Lucas Piessevaux | Periodic cyclic homology and global prismatic complexes |
| 18.01 | Niklas Kipp | The first Chern class |
| 25.01 | Vova Sosnilo | Comparison with étale cohomology |
| 01.01 | — | — |
| 08.02 | Niklas Kipp | Calculations in syntomic cohomology |