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.

If you are interested in participating in this seminar, please contact Marc Hoyois or Denis Nardin.

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
08.02 Niklas Kipp Calculations in syntomic cohomology