$\newcommand\A{\mathrm{A}} \newcommand\C{\mathrm{C}} \newcommand\D{\mathrm{D}} \newcommand\E{\mathrm{E}} \newcommand\F{\mathrm{F}} \newcommand\G{\mathrm{G}} \newcommand\H{\mathrm{H}} \newcommand\h{\mathrm{h}} \newcommand\K{\mathrm{K}} \newcommand\L{\mathrm{L}} \newcommand\M{\mathrm{M}} \newcommand\t{\mathrm{t}} \newcommand{\bA}{\mathbf{A}} \newcommand{\bG}{\mathbf{G}} \newcommand{\bH}{\mathbf{H}} \newcommand{\bT}{\mathbf{T}} \newcommand{\bW}{\mathbf{W}} \newcommand{\Gm}{\bG_m} \newcommand\Ascr{\mathcal{A}} \newcommand\Cscr{\mathcal{C}} \newcommand\Dscr{\mathcal{D}} \newcommand\Escr{\mathcal{E}} \newcommand\Kscr{\mathcal{K}} \newcommand\Lscr{\mathcal{L}} \newcommand\Oscr{\mathcal{O}} \newcommand\Perfscr{\mathcal{P}\mathrm{erf}} \newcommand\Acscr{\mathcal{A}\mathrm{c}} \newcommand\heart{\heartsuit} \newcommand\cn{\mathrm{cn}} \newcommand\op{\mathrm{op}} \newcommand\gr{\mathrm{gr}} \newcommand\Gr{\mathrm{Gr}} \newcommand\fil{\mathrm{fil}} \newcommand\Ho{\mathrm{Ho}} \newcommand\dR{\mathrm{dR}} \newcommand\HH{\mathrm{HH}} \newcommand\HC{\mathrm{HC}} \newcommand\HP{\mathrm{HP}} \newcommand\TC{\mathrm{TC}} \newcommand{\bMap}{\mathbf{Map}} \newcommand{\End}{\mathrm{End}} \newcommand{\Mod}{\mathrm{Mod}} \newcommand{\coMod}{\mathrm{coMod}} \newcommand{\Fun}{\mathrm{Fun}} \newcommand{\bMap}{\mathbf{Map}} \newcommand\bE{\mathbf{E}} \newcommand\bZ{\mathbf{Z}} \newcommand\bAM{\mathbf{AM}} \newcommand\bLM{\mathbf{LM}} \newcommand\Spec{\mathrm{Spec}} \newcommand\CAlg{\mathrm{CAlg}} \newcommand\aCAlg{\mathfrak{a}\CAlg} \newcommand\dCAlg{\mathfrak{d}\CAlg}$

We will follow, with some minor modifications, the Bonn syllabus from one year ago to study the paper on prismatic Dieudonn'e theory from Anschütz and Le Bras [1], concluding with an addendum for Mondal’s paper [3] on the stacky approach to the theory.

The seminar meets from 1300 to 1500 central time on Thursdays.

Syllabus

Talk 1 (01/14). Classical Dieudonné theory over perfect fields of characteristic $p>0$ . Bao Le Hung.

Talk 2 (01/21). The crystalline Dieudonné module. Benjamin Antieau.

Talk 3 (01/28). Dieudonné theory over perfect rings of characteristic $p>0$ . Micah Darrell.

Talk 4 (skip). Dieudonné theory over $\Oscr_C$ .

Talk 5 (02/04). Prisms and perfectoid rings. Eivind Hjelle.

Talk 5.5 (02/04). Prismatic cohomology. Go over the main results of the Bhatt-—Scholze paper [2] on prismatic cohomology. Carlos Cortez.

Talk 6 (02/11). Filtered prismatic Dieudonné crystals. Elchanan Nafcha.

Talk 7 (02/18). Definition of the functor. Joel Stapleton.

Talk 8 (02/18). Finiteness results. Deven Manam.

Talk 9 (02/25). The $q$ -logarithm. Adam Holeman.

Talk 10 (03/04). Fully faithfulness. Kirill Magidson.

Talk 11 (03/11). Essential surjectivity. Adam Holeman.

Talk 12 (03/18). Mondal’s paper [3]. Artem Prikhodko.

References

[1] Anschütz and Le Bras, Prismatic Dieudonné theory, arXiv:1907.10525.

[2] Bhatt and Scholze, Prisms and prismatic cohomology, arXiv:1905.08229.

[3] Mondal, Dieudonné theory via cohomology of classifying stacks, arXiv:2002.05413.