Related papers: Groupes p-divisibles, groupes finis et modules fil…

Let $k$ be a perfect field of characteristic $p > 2$. We extend the equivalence of categories between Fontaine-Laffaille modules and $\mathbb{Z}_p$ lattices inside crystalline representations with Hodge-Tate weights at most $p-2$ of…

Let $\mathscr{O}_K$ be a 2-adic discrete valuation ring with perfect residue field $k$. We classify $p$-divisible groups and $p$-power order finite flat group schemes over $\mathscr{O}_K$ in terms of certain Frobenius module over…

Assume that $p>2$, and let $\mathscr{O}_K$ be a $p$-adic discrete valuation ring with residue field admitting a finite $p$-basis, and let $R$ be a formally smooth formally finite-type $\mathscr{O}_K$-algebra. (Indeed, we allow slightly more…

For a prime number p>2, we give a direct proof of Breuil's classification of killed by p finite flat group schemes over the valuation ring of a p-adic field with perfect residue field. As application we prove that the Galois modules of…

Let $k$ be a perfect field of characteristic $p$ and $W(k)$ its ring of Witt vectors. We construct an equivalence of categories between the full subcategory of the derived category of quasi-coherent sheaves on the syntomification of $W(k)$…

Let $k$ be a perfect field of characteristic $p>2$ and $K$ an extension of $F=\mathrm{Frac} W(k)$ contained in some $F(\mu_{p^r})$. Using crystalline Dieudonn\'e theory, we provide a classification of $p$-divisible groups over…

A p-divisible group over a complete local domain determines a Galois representation on the Tate module of its generic fibre. We determine the image of this representation for the universal deformation in mixed characteristic of a…

Building on foundations introduced in a previous paper, we give several p-adic analytic descriptions of the categories of etale Zp-local systems and etale Qp-local systems on an affinoid algebra over a finite extension of Qp (or more…

We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $p$-adic representations of the absolute Galois groups of $p$-adic fields under the assumptions that $p$ is odd and the coefficients…

Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A)…

Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was introduced recently by Faltings and appears as an equal characteristic analogue of the…

Let K be a complete discretely valued field of mixed characteristics (0, p) with perfect residue field. One of the central objects of study in p-adic Hodge theory is the category of continuous representations of the absolute Galois group of…

We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of…

For a smooth formal scheme $\mathfrak{X}$ over the Witt vectors $W$ of a perfect field $k$, we construct a functor $\mathbb{D}_\mathrm{crys}$ from the category of prismatic $F$-crystals $(\mathcal{E},\varphi_\mathcal{E})$ (or prismatic…

Let p be an odd prime. We show that the classification of p-divisible groups by Breuil windows and the classification of finite flat group schemes of p-power order by Breuil modules hold over any complete regular local ring with perfect…

We study the notion of Wach modules in relative setting, generalizing the arithmetic case. Over an unramified base, for a $p$-adic representation admitting such structure, we examine the relationship between its relative Wach module and…

Let R be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a…

Let $G$ be a split reductive group over the ring of integers in a $p$-adic field with residue field $\mathbf{F}$. Fix a representation $\overline{\rho}$ of the absolute Galois group of an unramified extension of $\mathbf{Q}_p$, valued in…

As an extension of previous ungraded work, we define a graded $p$-polar ring to be an analog of a graded commutative ring where multiplication is only allowed on $p$-tuples (instead of pairs) of elements of equal degree. We show that the…

This paper is a summary of author's results on finite flat commutative group schemes. The properties of the generic fibre functor are discussed. A complete classification of finite local flat commutative group schemes over mixed…