Related papers: On categories of (phi, Gamma)-modules

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

Let $K$ be a finite extension of $\mathbb{Q}_p$, and $\rho$ be an $n$-dimensional (non-critical generic) crystabelline representation of the absolute Galois group of $K$ of regular Hodge-Tate weights. We associate to $\rho$ an explicit…

We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined…

We describe the structure of the Whittaker or Gelfand-Graev module on a $n$-fold metaplectic cover of a $p$-adic group $G$ at both the Iwahori and spherical level. We express our answer in terms of the representation theory of a quantum…

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…

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-etale site, which makes all constructions…

In this paper we interpret the solutions to a particular Galois embedding problem over an extension K/F whose Galois group is a finite, cyclic p group in terms of certain Galois submodules within the parameterizing space of elementary…

Let K be a p-adic local field with residue field k such that [k:k^p]=p^e<\infty and V be a p-adic representation of Gal(\bar{K}/K). Then, by using the theory of p-adic differential modules, we show that V is a potentially crystalline (resp.…

Let $\mathbf{G}$ be a connected reductive group over a finite field $\mathbb{F}_q$ of characteristic $p > 0$. In this paper, we study a category which we call Deligne--Lusztig category $\mathcal{O}$ and whose definition is similar to…

In this paper we continue the study of locally analytic representations of a $p$-adic Lie group $G$ in vector spaces over a spherically complete non-archimedean field $K$, building on the algebraic approach to such representations…

We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding Kac-Moody 2-category (and vice versa). This…

This paper develops a representation-theoretic approach to the isogeny category $\underline{\mathcal{C}}$ of commutative group schemes of finite type over a field $k$, studied in arXiv:1602:00222. We construct a ring $R$ such that…

We relate two different proposals to extend the \'etale topology into homotopy theory, namely via the notion of finite cover introduced by Mathew and via the notion of separable commutative algebra introduced by Balmer. We show that finite…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

Let $ k $ be a field, $ G $ a totally ordered abelian group and $ \mathbb K = k((G)) $ the maximal field of generalised power series, endowed with the canonical valuation $ v $. We study the group $ v \mathrm{-Aut} K $ of valuation…

We continue the examination of the stable reduction and fields of moduli of G-Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup P of order…

We give a new construction of $p$-adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The definition is analytic, closely resembling that of complex…

We investigate infinite dimensional modules for a linear algebraic group $\mathbb G$ over a field of positive characteristic $p$. For any subcoalgebra $C \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we consider…

One of the main themes of this long article is the study of projective varieties which are K(H,1)'s, i.e. classifying spaces BH for some discrete group H. After recalling the basic properties of such classifying spaces, an important class…