Related papers: Perfect algebraic stacks

We develop a theory of perfect algebraic spaces that extend the so-called perfect schemes to the setting of algebraic spaces. We prove several desired properties of perfect algebraic spaces. This extends some previous results of perfect…

This paper is a subsequent paper of arXiv:2303.07672. We will continue our research on the subject of perfect algebraic spaces that is developed in arXiv:2303.07672. By means of algebraic Frobenius morphisms, we define the perfection of…

One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by…

We prove Grothendieck's existence theorem for relatively perfect complexes on an algebraic stack that is proper and flat over an $I$-adically complete Noetherian ring $A$. This generalizes an earlier result of Lieblich in the setting of…

With the long-term goal of proving local structure theorems of algebraic stacks in positive characteristic near points with reductive (but possibly non-linearly reductive) stabilizer, we conjecture that quotient stacks of the form…

We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or…

We show that every quasi-compact and quasi-separated algebraic stack can be approximated by a noetherian algebraic stack. We give several applications such as eliminating noetherian hypotheses in the theory of good moduli spaces.

We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…

This work studies $t$-structures for the derived category of quasi-coherent sheaves on a quasi-compact quasi-separated algebraic stack. Specifically, using Thomason filtrations, we classify those $t$-structures which are generated by…

Let \pi : X -> S be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers. We prove that there is an algebraic S-stack, the Hilbert stack, parameterizing proper algebraic stacks mapping quasi-finitely…

This is an expended and revised version of the preprint "Schematization of homotopy types". The purpose of this work is to introduce a notion of \emph{affine stacks}, which is a homotopy version of the notion of affine schemes, and to give…

To, say, a proper algebraic or holomorphic space $X/S$, and a coherent sheaf ${\mathcal F}$ on $X$ we identify a functorial ideal, the fitted flatifier, blowing up sequentially in which leads to a flattening of the proper transform of…

The categories of almost modules and almost algebras are introduced as a convenient setting for the development of Faltings' method of almost etale extensions. After some preliminaries of general "almost homological algebra" we construct…

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…

The aim of this paper is to extend the definition of motivic homotopy theory from schemes to a large class of algebraic stacks and establish a six functor formalism. The class of algebraic stacks that we consider includes many interesting…

A perfect structure is a triple $(M,P,S)$ of matrices $M, P$ and $S$ of consistent sizes such that $MP = PS$. Perfect structures comprise similar matrices, eigenvectors, perfect colorings (equitable partitions) and graph coverings. In this…

Using Balmer--Favi's generalized idempotents, we establish the telescope conjecture for many algebraic stacks. Along the way, we classify the thick tensor ideals of perfect complexes of stacks.

Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps.…

To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of…

Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as…