Related papers: An abelian embedding for Moore spectra

Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this paper, we use condensed mathematics…

We classify abelian subgroups of two-dimensional Artin groups.

We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelopes are characterized in terms of those extension groups. We…

By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some…

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for…

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.

We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone…

We show that the quotient of the continuous cluster category $\mathcal C_\pi$ modulo the additive subcategory generated by any cluster is an abelian category and we show that it is isomorphic to the category of infinite length modules over…

We construct an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G and show it is of finite injective dimension. It can be used as a model for rational $G$-spectra in the sense that there is a homology…

In a stable abelian group, we characterize generic types of cosets of type-definable subgroups.

We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these varieties as well as the containments between them.

For flat proper families of algebraic varieties with a smooth fiber, we describe the abelian category of coherent sheaves on the generic fiber as a Serre quotient. As an application, we prove specialization of derived equivalence. As…

Let $\mathcal{S}$ be a small category, and suppose that we are given a full subcategory $\mathcal{U}$ such that every object of $\mathcal{S}$ can be embedded into some object of $\mathcal{U}$ in the same way as every quasi-projective…

We explicitly construct the algebraic model of affine Jacobian of a generic algebraic curve of high genus and use it to compute the Euler characteristic of the Jacobian and investigate its structure.

We discuss some aspects of the theory of subelliptic estimates.

Let $C$ be a smooth irreducible affine curve $C$ over an algebraically closed field of positive characteristic and let $\pi_1(C)$ be its fundamental group. We study various embedding problems for $\pi_1(C)$ and its subgroups.

In this paper, we examine an analogue of the recently solved spectrum conjecture by Fujita in the setting of Fine polyhedral adjunction theory. We present computational results for lower-dimensional polytopes, which lead to a complete…

We introduce the concept of a pseudo-cluster tilting subcategory from the viewpoint of the fact that the quotient of an exact category by a cluster tilting subcategory is an abelian category. We prove that the quotients in the case of…

We define the notion of a submersion of subcartesian differential spaces and prove some of its properties, which are analogous to those of a submersion in the category of smooth manifolds and smooth mappings.

We consider categorical and geometric purity for sheaves of modules over a scheme satisfying some mild conditions, both for the category of all sheaves and for the category of quasicoherent sheaves. We investigate the relations between…