Related papers: Classicality of derived Emerton-Gee stack

We use the Tannakian formalism to define the Emerton--Gee stack for general groups. For a flat algebraic group G over Z_p, we are able to prove the associated Emerton--Gee stack is a formal algebraic stack locally of finite presentation…

Let $K / \mathbb{Q}_p$ be a finite unramified extension, and let $\mathcal{X}_n$ denote the Emerton-Gee stack parametrizing \'etale $(\varphi,\Gamma_K)$-modules of rank $n$. It is known since the work of Emerton-Gee that the irreducible…

We give a classification of rank one $(\varphi,\Gamma)$-modules with coefficients in a $p$-adically complete $\mathbf{Z}_p$-algebra. As a consequence, we obtain a new proof of Proposition 7.2.17 in {arXiv:1908.07185}, which gives an…

We construct a moduli stack of rank 4 symplectic projective \'etale $(\varphi,\Gamma)$-modules and prove its geometric properties for any prime $p>2$ and finite extension $K/\mathbf{Q}_p$. When $K/\mathbf{Q}_p$ is unramified, we adapt the…

These are notes on derived algebraic geometry in the context of animated rings. More precisely, we recall the proof of To\"en-Vaqui\'e that the derived stack of perfect complexes is locally geometric in the language of $\infty$-categories.…

Let $K$ be a finite unramified extension of $\mathbb{Q}_p$, where $p>2$. [CEGS22b] and [EG23] construct a moduli stack of two dimensional mod $p$ representations of the absolute Galois group of $K$. We show that most irreducible components…

Let $F$ be an arbitrary $p$-adic field and let $G$ be an arbitrary reductive group over $F$ with Langlands dual group $^LG$. We show that the change-of-group morphism of Emerton-Gee stacks $\mathcal{X}_{^LG}\to\mathcal{X}_{GL_d}$ is…

Let $K$ be a finite unramified extension of $\mathbb{Q}_p$ with $p > 3$. We study the extremely non--generic irreducible components in the reduced part of the Emerton--Gee stack for $\mathrm{GL}_2$. We show precisely which irreducible…

Let $F/{\mathbb Q}_p$ be a finite unramified extension, let $k$ be a finite extension of the residue field of $F$. We provide explicit constructions of integral structures for all rank two \'{e}tale Lubin-Tate $(\varphi,{\mathcal…

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. The main result in this paper is an explicit calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an…

We construct a certain topological algebra $\Ext ^{\sharp}_{G ^{\vee}} X (\chi)$ from a Deligne-Langlands parameter space $X (\chi)$ attached to the group of rational points of a connected split reductive algebraic group $G$ over a…

We define derived versions of $F$-zips and associate a derived $F$-zip to any proper, smooth morphism of schemes in positive characteristic. We analyze the stack of derived $F$-zips and certain substacks. We make a connection to the…

For a separated scheme $X$ of finite type over a perfect field $k$ of characteristic $p>0$ which admits an immersion into a proper smooth scheme over the truncated Witt ring $W_{n}$, we define the bounded derived category of locally…

In the first part of this paper we construct a model structure for the category of filtered cochain complexes of modules over some commutative ring $R$ and explain how the classical Rees construction relates this to the usual projective…

The Deligne-Langlands correspondence parametrizes irreducible representations of the affine Hecke algebra $\mathcal{H}^{\text{aff}}$ by certain perverse sheaves. We show that this can be lifted to an equivalence of triangulated categories.…

Let $\Lambda$ be a complete noetherian local ring with finite residue field of characteristic $p$ and $K/\mathbb{Q}_p$ a $p$-adic field. We show that, by deformation of the structure sheaf on the (transversal) prismatic site of a bounded…

This paper investigates the derived and spectral analogs of logarithmic geometry. We develop the deformation theory for animated log rings and $\mathbb{E}_\infty$-log rings and examine the corresponding theories of derived and spectral log…

We show that any $(-2)$-shifted symplectic derived scheme $\textbf{X}$ (of finite type over an algebraically closed field of characteristic zero) is locally equivalent to the derived intersection of two Lagrangian morphisms to a…

Let $p$ be a fixed odd prime, and let $K$ be a finite extension of $\mathbb{Q}_p$ with ring of integers $\mathcal{O}_K$. The Emerton-Gee stack for $\mathrm{GL}_2$ is a stack of $(\varphi, \Gamma)$-modules. The stack, denoted…

In this article, we derive many properties of \'etale stacks in various contexts, and prove that \'etale stacks may be characterized categorically as those stacks that arise as prolongations of stacks on a site of spaces and local…