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Learning Seminar on Prismatic Cohomology


Time: Friday 2:00 PM - 3:30 PM
Location: CDS 548

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Zoom link: https://bostonu.zoom.us/j/3839807917

This is a learning seminar on prismatic cohomology. The main goal is to introduce the basiscs of prismatic cohomology following Bhatt-Scholze and conclude with discussions on Guo-Reinecke's approach to the C_crys conjecture for any crystalline local systems over any smooth proper p-adic rigid analytic space. Most of the talks will be given by the organizer (Xinyu). But I will be very happy if people volunteer to give talks (on topics listed below or other related topics). Anyone is welcome to join. Just remeber to fill out the mailing list form linked above! I also listed some possible additional topics below.

References

  1. Bhargav Bhatt and Peter Scholze. "Prisms and prismatic cohomology." Ann. of Math. (2) 196 (3) 1135 - 1275, November 2022.
  2. Bhargav Bhatt. Eilenberg Lectures on Prismatic cohomology.
  3. Kiran Kedlaya. Notes on prismatic cohomology .
  4. Haoyang Guo and Emanuel Reinecke. "A Prismatic Approach to Crystalline Local Systems." Inventiones Mathematicae. 236, 17-164 February 2024.

Schedule

Week Date Topic Speaker Notes
Week 1 Apr 25 delta-rings, derived completion, and prisms Xinyu Notes.
Week 2 May 2 Prismatic site and Hodge-Tate comparison Xinyu Notes.
Week 3 May 9 Derived prismatic cohomology, etale comparison Ashutosh
Week 4 May 16 Cancelled
Week 5 May 23 q-de Rham cohomology Xinyu
Week 6 May 30 Cancelled
Week 7 June 6 A Prismatic Approach to Crystalline Local Systems Xinyu Prepared notes. Meeting notes.
Week 8 June 13 An arithmetic étale-crystalline comparison with coefficients in crystalline local systems Zachary
Week 9 June 20 Prismatic Dieudonne Theory James
Week 10 June 27 Essential Dimensions via Prismatic Cohomology Ashutosh

Some additional topics (beyond Bhatt-Scholze)

Topic 1: An arithmetic etale-crystalline comparison with coefficients in crystalline local systems
Reference: Maximilian Hauck https://arxiv.org/abs/2505.03294

Topic 2: Prismatic Dieudonne Theory
Reference: Anschütz J, Le Bras A-C. Prismatic Dieudonne Theory. Forum of Mathematics, Pi. 2023;11:e2

Topic 3: Absolute Prismatic Cohomology
Reference: Bhatt, Bhargav, and Jacob Lurie. 2022. Absolute Prismatic Cohomology. arXiv link..

Topic 4: Essential Dimension via Prismatic Cohomology
Reference: arb, Benson, Mark Kisin, and Jesse Wolfson. 2024. Essential Dimension via Prismatic Cohomology. arXiv link..

Topic 5: Dieudonné theory via cohomology of classifying stacks.
Reference: Mondal S. Dieudonné theory via cohomology of classifying stacks. Forum of Mathematics, Sigma. 2021;9:e81