Related papers: Automorphic Gluing

In the setting of the geometric Langlands conjecture, we argue that the phenomenon of divergence at infinity on Bun_G (that is, the difference between $!$-extensions and $*$-extensions) is controlled, Langlands-dually, by the locus of…

Let $\mathcal{C}$ be a representable 2-category, and $\mathfrak{T}_\bullet$ a 2-endofunctor of the arrow 2-category $\mathcal{C}^\downarrow$ such that (i) $\mathsf{cod} \mathfrak{T}_\bullet = \mathsf{cod}$ and (ii) $\mathfrak{T}_\bullet$…

We give a general proof of Shahidi's tempered L-function conjecture, which has previously been known in all but one case. One of the consequences is the standard modules conjecture for p-adic groups, which means that the Langlands quotient…

Given two automorphisms of a group $G$, one is interested in knowing whether they are conjugate in the automorphism group of $G$, or in the abstract commensurator of $G$, and how these two properties may differ. When $G$ is the fundamental…

We prove 2-categorical conservativity for any {0,T}-free fragment of MALL over its corresponding intuitionistic version: that is, that the universal map from a closed symmetric monoidal category to the *-autonomous category that it freely…

Let $G=\mathbf{Z}_{p} \oplus \mathbf{Z}_{p^2}$, where $p$ is a prime number. Suppose that $d$ is a divisor of the order of $G$. In this paper we find the number of automorphisms of $G$ fixing $d$ elements of $G$, and denote it by…

Given a homological epimorphism $\pi:\mathcal{C}\longrightarrow \mathcal{C}/\mathcal{I}$ between $K$-categories, we show that if the ideal $\mathcal{I}$ satisfies certain conditions, then there exists an equivalence between the singularity…

We establish the compatibility of the Langlands functor with the operations of Eisenstein series constant term, and deduce that the Langlands functor induces an equivalence on Eisenstein-generated subcategories.

Let $(\mbox{mod} \Lambda',\mbox{mod} \Lambda,\mbox{mod} \Lambda'')$ be a recollement of module categories for artin algebras $\Lambda'$, $\Lambda$ and $\Lambda''$. We provide a sufficient condition such that a glued torsion pair in…

Categories of models of algebraic theories have good categorical properties except for gluing. Building upon insights and examples from Synthetic Differential Geometry, we introduce a generalisation of models of algebraic theories to…

Let $\mathcal{M}$ be an $n$-cluster tilting subcategory of ${\rm mod}\mbox{-}\Lambda$, where $\Lambda$ is an artin algebra. Let $\mathcal{S}(\mathcal{M})$ denotes the full subcategory of $\mathcal{S}(\Lambda)$, the submodule category of…

Gluing of two pseudo functors has been studied by Deligne, Ayoub, and others in the construction of extraordinary direct image functors in \'etale cohomology, stable homotopy, and mixed motives of schemes. In this article, we study more…

Let G be a compact Lie group and X be a compact smooth G-manifold with finitely many G-fixed points. We show that if X admits a G-equivariant hyperbolic diffeomorphism having a certain convergence property, there exists an open covering of…

If $\mathbf{C}$ is a category with pullbacks then there is a bicategory with the same objects as $\mathbf{C}$, spans as morphisms, and maps of spans as 2-morphisms, as shown by Benabou. Fong has developed a theory of "decorated" cospans,…

We establish a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic surfaces in static vacuum four-dimensional backgrounds with cosmological constant $\Lambda \in \mathbb{R}$ and arbitrary…

The object of this paper is to prove that the standard categories in which homotopy theory is done, such as topological spaces, simplicial sets, chain complexes of abelian groups, and any of the various good models for spectra, are all…

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…

Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank r and fixed determinant \Lambda, of degree d. We give a new proof of the fact that…

We prove a combinatorial rule for a complete decomposition, in terms of Langlands parameters, for representations of p-adic $GL_n$ that appear as parabolic induction from a large family (ladder representations). Our rule obviates the need…

We prove a version of quantum geometric Langlands conjecture in characteristic $p$. Namely, we construct an equivalence of certain localizations of derived categories of twisted crystalline $\mathcal D$-modules on the stack of rank $N$…