Time:

13:00-14:00 (Beijing Time), Oct. 9

Venue: online

Zoom number：93677314907

Pass code：121981

Abstract:

 Nowadays prismatic crystals are gathering an increasing interest as they unify various coefficients in $p$-adic cohomology theories. Recently, attached to any $p$-adic formal scheme $X$, Drinfeld and Bhatt-Lurie constructed certain ring stacks, including the prismatization of $X$, on which quasi-coherent complexes correspond to various crystals on the prismatic site of $X$. While such a stacky approach sheds some new light on studying prismatic crystals, little is known outside of the Hodge-Tate locus. In this talk, we will introduce our recent work on studying quasi-coherent complexes on certain nilpotent thickenings of the Hodge-Tate stack, with an eye towards their realizations as representations of $G_K$ when $X=\operatorname{Spf}(\mathcal{O}_K)$. As a byproduct, we classify certain truncated-prismatic crystals on the (relative/absolute) prismatic site of $X$.