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We define, for each quasi-syntomic ring $R$ (in the sense of Bhatt-Morrow-Scholze), a category $mathrm{DF}(R)$ of textit{filtered prismatic Dieudonne crystals over $R$} and a natural functor from $p$-divisible groups over $R$ to $mathrm{DF}(R)$. We prove that this functor is an antiequivalence. Our main cohomological tool is the prismatic formalism recently developed by Bhatt and Scholze.
We establish an arithmetic intersection theory in the framework of Arakelov geometry over adelic curves. To each projective scheme over an adelic curve, we associate a multi-homogenous form on the group of adelic Cartier divisors, which can be writte
Let $(A, I)$ be a bounded prism, and $X$ be a smooth $p$-adic formal scheme over $Spf(A/I)$. We consider the notion of crystals on Bhatt--Scholzes prismatic site $(X/A)_{prism}$ of $X$ relative to $A$. We prove that if $X$ is proper over $Spf(A/I)$ o
This is a survey based on the construction of Siegel modular forms of degree 2 and 3 using invariant theory in joint work with Fabien Clery and Carel Faber.
A qualgebra $G$ is a set having two binary operations that satisfy compatibility conditions which are modeled upon a group under conjugation and multiplication. We develop a homology theory for qualgebras and describe a classifying space for it. This
The isomorphism number (resp. isogeny cutoff) of a p-divisible group D over an algebraically closed field is the least positive integer m such that D[p^m] determines D up to isomorphism (resp. up to isogeny). We show that these invariants are lower s