Related papers: Locally finitely presented and coherent hearts

We show that if $\alpha$ is a regular cardinal, $\mathcal{D}$ is an $\alpha$-compactly generated triangulated category, in the sense of Neeman \cite{N}, and $\tau$ is a t-structure in $\mathcal{D}$ generated by a set of $\alpha$-compact…

Classical definitions of locally complete intersection (l.c.i.) homomorphisms of commutative rings are limited to maps that are essentially of finite type, or flat. The concept introduced in this paper is meaningful for homomorphisms phi :…

For a self-orthogonal module $T$, the relation between the quotient triangulated category $D^b(A)/K^b({\rm add} T)$ and the stable category of the Frobenius category of $T$-Cohen-Macaulay modules is investigated. In particular, for a…

Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. Here, we show that, in the Serre subcategories of the category of $R$--modules, how the…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $\mathcal{D}(R)$ denote the derived category of $R$-modules. We investigate the theory of local homology in conjunction with Gorenstein flat modules. Let $X$ be a…

In this paper, we study ICE-closed (= Image-Cokernel-Extension-closed) subcategories of an abelian length category using torsion classes. To each interval $[\mathcal{U},\mathcal{T}]$ in the lattice of torsion classes, we associate a…

Let $R=\bigoplus_{n\geq 0}R_n$, $\fa\supseteq \bigoplus_{n> 0}R_n$ and $M$ and $N$ be a standard graded ring, an ideal of $R$ and two finitely generated graded $R$-modules, respectively. This paper studies the homogeneous components of…

Our main goal in this paper is to answer new positive cases of the natural generalized version of Hartshorne's celebrated question on cofiniteness of local cohomology modules, and consequently of Huneke's conjecture on the finiteness of…

We prove a sheaf-theoretic derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendieck's local duality theorem): for a quasi-compact separated scheme X and a "proregular" subscheme Z---for…

If $H$ is a lattice in a locally compact second countable group $G$, then we show that $G$ has property A (respectively is coarsely embeddable into Hilbert space) if and only if $H$ has property A (respectively is coarsely embeddable into…

For any cohomology theory $H$ that can be factorized through (the Morel-Voevodsky's triangulated motivic homotopy category) $SH^{S^1}(k)$ we establish the $SH^{S^1}(k)$-functoriality of coniveau spectral sequences for $H$. We also prove:…

This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are…

Condensed mathematics as developed by Clausen and Scholze yields a version of derived functors over the category of continuous $G$-modules for a Hausdorff topological group $G$. We study the resulting notion of group cohomology and its…

We introduce the notions of categorical integrals and categorical cointegrals of a finite tensor category $\mathcal{C}$ by using a certain adjunction between $\mathcal{C}$ and its Drinfeld center $\mathcal{Z}(\mathcal{C})$. These notions…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $M$ a finitely generated $R$--module. Let $t$ be a non-negative integer such that $\H^i_\fa(M)$ is $\fa$--cofinite for all $i<t$. It is well--known that…

In this paper, we study when the kernel of a complete hereditary cotorsion pair is the additive closure of a tilting module. Applications go in three directions. The first is to characterize when the little finitistic dimension is finite.…

We give a local treatment of finite alignment by identifying the finitely aligned part of any (not necessarily finitely aligned) higher-rank graph. We show the finitely aligned part is itself a constellation and forms a finitely aligned…

We give a classification of all exact structures on a given idempotent complete additive category. Using this, we investigate the structure of an exact category with finitely many indecomposables. We show that the relation of the…

This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebraic topology. In it, we show that the \v{C}ech cohomology…

Let $G$ be a connected semisimple algebraic group over an algebraically closed field $k$. In 1965 Steinberg proved that if $G$ is simply connected, then in $G$ there exists a closed irreducible cross-section of the set of closures of…