Related papers: Height 1 Group Schemes and Prismatic F-Gauges

In this paper, we apply stack theoretic ideas to the classification problem in Dieudonn\'e theory. First, we use crystalline cohomology of classifying stacks to directly reconstruct the classical Dieudonn\'e module of a finite, $p$-power…

We show an equivalence of categories, over general $p$-adic bases, between finite locally $p^n$-torsion commutative group schemes and $\Int/p^n\Int$-modules in perfect $F$-gauges of Tor amplitude $[-1,0]$ with Hodge-Tate weights $0,1$. By…

We prove that if $G$ is a finite flat group scheme of $p$ power rank over a perfect field of characteristic $p$, then the second crystalline cohomology of its classifying stack $H^2_{crys}(BG)$ recovers the Dieudonn\'e module of $G$. We…

For a smooth affine group scheme $G$ over the ring of $p$-adic integers $\mathbb{Z}_p$ and a cocharacter $\mu$ of $G$, we study $G$-$\mu$-displays over the prismatic site of Bhatt-Scholze. In particular, we obtain several descent results…

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…

For certain contractible G-CW-complexes and F a family of subgroups of G, we construct a spectral sequence converging to the F-Bredon cohomology of G with E1-terms given by the F-Bredon cohomology of the stabilizer subgroups. As…

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…

The paper is concerned with Kropholler's conjecture on splitting a finitely generated group over a codimension-1 subgroup. For a subgroup H of a group G, we define the notion of "finite splitting height" which generalises the finite-height…

For a $p$-divisible group $G$ over a smooth projective variety $X$ over $k$, where $k$ is a field finitely generated over a perfect field of characteristic $p$, we show that the formal group $R^i f_{\fppf*} G$ is isogenous to a…

In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the…

We prove various finiteness and representability results for cohomology of finite flat abelian group schemes. In particular, we show that if $f\colon X\rightarrow \mathrm{Spec}(k)$ is a projective scheme over a field $k$ and $G$ is a finite…

We develop a new cohomology theory in characteristic p>0, the so called F-gauge cohomology, a cohomology with values in the category of so-called F-gauges, which refines the cristalline cohomology. In this first paper we mainly discuss the…

For a smooth $p$-adic formal scheme over the ring of integers of a perfectoid field of mixed characteristic $(0,p)$ containing all $p$-power roots of unity, we prove that the prismatic cohomology of a locally finite free prismatic crystal…

Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…

Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a $q$-Higgs module and the associated $q$-Higgs complex on the bounded prismatic envelope of an embedding…

For a split reductive group $G$ we realise identities in the Grothendieck group of $\widehat{G}$-representation in terms of cycle relations between certain closed subschemes inside the affine grassmannian. These closed subschemes are…

We study the combinatorics of the category F of finite-dimensional modules for the orthosymplectic Lie supergroup OSP(r|2n). In particular we present a positive counting formula for the dimension of the space of homomorphism between two…

Let $S$ be an fs log scheme, and let $F$ be a group scheme over the underlying scheme which is \'etale locally representable by (1) a finite dimensional $\mathbb{Q}$-vector space, or (2) a finite rank free abelian group, or (3) a finite…

We discuss the relation between crystalline Dieudonne theory and Dieudonne displays, with special emphasis on the case p=2. The theory of Dieudonne displays is extended to this case without restriction, which implies that the classification…