Related papers: Semi-factorial models and N\'eron models

For a regular normal element in an arbitrary ring, we study the category of its module factorizations. The cokernel functor relates module factorizations with Gorenstein projective components to Gorenstein projective modules over the…

In this paper, we investigate the properties of $A$-coherent and $A$-quasi-coherent sheaves within the framework of algebraic geometry over non-algebraically closed fields. We define an $\mathcal{O}_X$-module to be $A$-coherent (resp.…

Kuznetsov showed that for a flat quadric fibration $\mathcal{Q}$ over a smooth base $S$, $\mathrm{D}^b(\mathcal{Q})$ admits a semiorthogonal decomposition where one of the components is the derived category of the sheaf of even parts of a…

In this paper we provide several results regarding the structure of derived categories of (nested) Hilbert schemes of points. We show that the criteria of Krug-Sosna and Addington for the universal ideal sheaf functor to be fully faithful…

For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y --> X and the category of cocontinuous tensor functors…

We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable $\infty$-categories. Building on this, we study the relative Waldhausen S-construction $S_\bullet(F)$ of a spherical functor $F$ and…

We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…

An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…

We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…

We give regular models for modular curves associated with (normalizer of) split and non-split Cartan subgroups of ${\mathrm{GL}}_2 ({\mathbb F}_p )$ (for $p$ any prime, $p\ge 5$). We then compute the group of connected components of the…

For a smooth projective variety $X$ of dimension $d \geq 5$ over an algebraically closed field $k$ of characteristic zero, it is shown in this paper that the bounded derived category of the Hilbert scheme of three points $X^{[3]}$ admits a…

Let X be a smooth proper variety over the quotient field of a Henselian discrete valuation ring with algebraically closed residue field of characteristic p. We show that for any coherent sheaf E on X, the index of X divides the…

We study semiresolutions of quasi-projective varieties with properties $G_1$, $S_2$, and seminormality. Equivalently, these are varieties $X$ with Serre's $S_2$ property, such that there exists an open subvariety $U$, with complement of…

Let $S$ be a Noetherian scheme, and let $X$ be a scheme over $S$, such that all relative symmetric powers of $X$ over $S$ exist. Assume that either $S$ is of pure characteristic $0$ or $X$ is flat over $S$. Assume also that the structural…

We associate to every divisorial (e.g. smooth) variety $X$ with only constant invertible global functions and finitely generated Picard group a $Pic(X)$-graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate…

We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies the classical characterization of semi-invariants in terms of a differential operator. Then, we present a combinatorial…

We introduce the notion of pseudo-N\'eron model and give new examples of varieties admitting pseudo-N\'eron models other than Abelian varieties. As an application of pseudo-N\'eron models, given a scheme admitting a finite morphism to an…

Let X be a Hilbert bimodule over a C*-algebra A and $O_X= A \rtimes_X \Z$. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on $s_{\xi} s_{\eta}^*$…

Given an algebra $A$ over a differential field $K$, we study derivations on $A$ that are compatible with the derivation on $K$. There is a universal object, which is a twisted version of the usual module of differentials, and we establish…

We prove that any right Quillen functor between arbitrary model categories admits non trivial functorial factorizations that are similar to those of a model structure. We also prove that these factorizations can be made for lax monoidal…