Related papers: A note on \'etale endomorphisms of normal schemes

We prove that separable extensions of noetherian rings and finite \'etale morphisms of noetherian schemes give rise to separable extensions of singularity categories.

We define the category of \'etale Chow motives as the \'etale analogue of Grothendieck motives and proved that it embeds in $\text{DM}_{\text{\'et}}(k)$. This construction provides a characterization of the generalized Hodge conjecture in…

In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…

Recently, Cochran and Harvey defined torsion-free derived series of groups and proved an injectivity theorem on the associated torsion-free quotients. We show that there is a universal construction which extends such an injectivity theorem…

This note presents a uniform treatment of normality and three of its variants---topological, weak and seminormality---for Noetherian schemes. The key is to define these notions for pairs $(Z, X)$ consisting of a (not necessarily reduced)…

We show that every scheme/algebraic space/stack that is quasi-compact with quasi-finite diagonal can be approximated by a noetherian scheme/algebraic space/stack. More generally, we show that any stack which is etale-locally a global…

In this article, we show that a flat morphism of $k$-varieties ($\mathop{\mathrm{char}} k=0$) with locally constant geometric fibers becomes finite \'etale after reduction. When $k$ is a real closed field, we prove that such a morphism…

Let $f$ be an Anosov diffeomorphism of the $n$-dimensional torus ${\mathbb{T}}^n$ and $\tau$ a continuous self-mapping of ${\mathbb{T}}^n$ commuting with $f$. We prove that $\tau$ is surjective if and only if the restriction of $\tau$ to…

We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.

We study two notions of purity in categories of sheaves: the categorical and the geometric. It is shown that pure injective envelopes exist in both cases under very general assumptions on the scheme. Finally we introduce the class of…

Suppose that $(\mathcal{F},\mathcal{M})$ is an injective structure of $R$-Mod such that the class $\mathcal{F}$ is closed for direct limits, then two modules in $\mathcal{M}$ are isomorphic if there are maps in $\mathcal{F}$ from each one…

We prove that every smooth subelliptic variety admits a surjective morphism from an affine space. This result gives partial answers to the questions of Arzhantsev and Forstneri\v{c}. As an application, we characterize open images of…

We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential matrix.

We give a complete description of the derived equivalence normal forms of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings. As a consequence, a description of the…

Let S be a Noetherian scheme and f:X -> S a proper morphism. By SGA 4 XIV, for any constructible sheaf F of Z/nZ-modules on X, the sheaves of Z/nZ-modules R^if_*F obtained by direct image (for the etale topology) are also constructible:…

Let $Y$ be a normal and projective variety over an algebraically closed field $k$ and $V$ a vector bundle over $Y$. We prove that if there exist a $k$-scheme $X$ and a finite surjective morphism $g:X\to Y$ that trivializes $V$ then $V$ is…

The generalisation of the well-known (Hilbert polynomial) criterion for flatness of a projective morphism of Noetherian schemes is given for the case of nonreduced base of the morphism.

We prove that any commutative group scheme separated over a noetherian normal scheme admits a canonical structure of a presheaf with transfers, which is characterized by a simple condition on radicial transfers.

For a given arithmetic scheme, in this paper we will introduce and discuss the monodromy action on a universal cover of the \'etale fundamental group and the monodromy action on an \emph{sp}-completion constructed by the graph functor,…

Suppose that $X$ and $Y$ are surfaces of finite topological type, where $X$ has genus $g\geq 6$ and $Y$ has genus at most $2g-1$; in addition, suppose that $Y$ is not closed if it has genus $2g-1$. Our main result asserts that every…