Related papers: The Auslander-Gruson-Jensen Recollement

Let $R,S$ be rings, $\mathcal{X}\subseteq \text{mod}$-$R$ a covariantly finite subcategory, $\mathcal{C}$ the smallest definable subcategory of $\text{Mod}$-$R$ containing $\mathcal{X}$ and $\mathcal{D}$ a definable subcategory of…

Let $\Sigma$ be a small category and $\mathcal{A}$ be a $\Sigma$-co-complete (resp. $\Sigma$-complete) abelian category. It is a well-known fact that the category $\operatorname{Fun}(\Sigma,\mathcal{A})$ of functors of $\Sigma$ in…

In this paper we will prove that there exists a covariant functor, called algebraic anabelian functor, from the category of algebraic schemes over a given field to the category of outer homomorphism sets of groups. The algebraic anabelian…

The satellite endofunctors are used to extend the definition of linkage of ideals to the linkage of totally finitely presented functors. The new notion for linkage works over a larger class of rings and is consistent with the functorial…

We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class for us is the class of localizations which coincide with their zero derived…

Let $\mathbb{F}$ be a field and let $G\subset \mathbb{F}\setminus \{0\}$ be a multiplicative subgroup. We consider the category $\mathcal{Cob}_G$ of $3$-dimensional cobordisms equipped with a representation of their fundamental group in…

Let $A$ be an artin algebra. We show that the bounded homotopy category of finitely generated right $A$-modules has Auslander-Reiten triangles. Two applications are given: (1) we provide an alternative proof of a theorem of Happel in [H2];…

Let $U$ be a silting object in a derived category over a dg-algebra $A$, and let $B$ be the endomorphism dg-algebra of $U$. Under some appropriate hypotheses, we show that if $U$ is good, then there exist a dg-algebra $C$, a homological…

This paper is a complement to the paper "On $p$-adic differential equations on semistable varieties" written by V. Di Proietto. Given an open variety over a DVR with semistable reduction, the author constructed in that paper a fully…

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various…

We prove that the derived parabolic induction functor, defined on the unbounded derived category of smooth mod $p$ representations of a $p$-adic reductive group, admits a left adjoint $\mathrm{L}(U,-)$. We study the cohomology functors…

We give a proof of the Breuil-Schneider conjecture in a large number of cases, which complement the indecomposable case, which we dealt with earlier in [Sor]. In some sense, only the Steinberg representation lies at the intersection of the…

In this paper, we construct a version of Auslander-Reiten sequences for the $K(n)$-local stable homotopy category. In particular, the role of the Auslander-Reiten translation is played by the local Brown-Comenetz duality functor. As an…

Let $\mathfrak{g}$ and $\mathfrak{h}$ be two Lie algebras with $\mathfrak{h}$ finite dimensional and consider ${\mathcal A} = {\mathcal A} (\mathfrak{h}, \, \mathfrak{g})$ to be the corresponding universal algebra as introduced in…

Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of finitely presented functors $mod$-$\mathcal{M}$ modulo the subcategory of effaceable functors $mod_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory which…

In this paper we study adjunction relations between some natural functors on the representation category of the category of finite linearly ordered sets and order-preserving injections. We also prove that the Nakayama functor induces an…

Let $R$ be a commutative local ring. We study the subcategory of the homotopy category of $R$-complexes consisting of the totally acyclic $R$-complexes. In particular, in the context where $Q\to R$ is a surjective local ring homomorphism…

We associate to an arbitrary positive root $\alpha$ of a complex semisimple finite-dimensional Lie algebra $\mfrak{g}$ a twisting endofunctor $T_\alpha$ of the category of $\mfrak{g}$-modules. We apply this functor to generalized Verma…

Given a small abelian category $\mathcal{A}$, the Freyd-Mitchell embedding theorem states the existence of a ring $R$ and an exact full embedding $\mathcal{A} \rightarrow R$-Mod. This theorem is useful as it allows one to prove general…

Let $G$ be a connected reductive group over a non-archimedean local field $F$ of residue characteristic $p$, $P$ be a parabolic subgroup of $G$, and $R$ be a commutative ring. When $R$ is artinian, $p$ is nilpotent in $R$, and…