Related papers: On proper splinters in positive characteristic

Self-maps everywhere defined on the projective space $\P^N$ over a number field or a function field are the basic objects of study in the arithmetic of dynamical systems. One reason is a theorem of Fakkruddin \cite{Fakhruddin} (with…

Let $G$ be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic $p$. Let $I$ be a pro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobenius ring. If…

Let $R$ be a local ring of positive characteristic and $X$ a complex with nonzero finitely generated homology and finite injective dimension. We prove that if derived base change of $X$ via the Frobenius (or more generally, via a…

A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational…

In this note we first study regular $\mathbb{Z}$-graded local rings. We characterize commutative noetherian regular $\mathbb{Z}$-graded local rings in similar ways as in the usual local case. Then, we characterize graded isolated…

We prove that all projective crepant resolutions of Nakajima quiver varieties satisfying natural conditions are also Nakajima quiver varieties. More generally, we classify the small birational models of many Geometric Invariant Theory (GIT)…

In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over $\mathbb{Z}$ and over more general rings of integers $\mathcal{O}_K$, depending on their…

In this article we formulate and prove the main theorems of the theory of character sheaves on unipotent groups over an algebraically closed field of characteristic p>0. In particular, we show that every admissible pair for such a group G…

Given a 0-dimensional scheme $\mathbb{X}$ in the projective $n$-space $\mathbb{P}^n_K$ over a field $K$, we are interested in studying the K\"ahler different of $\mathbb{X}$ and its applications. Using the K\"ahler different, we…

Let X be a smooth projective variety over an algebraically closed field of positive characteristic. We prove that if D is a pseudo-effective R-divisor on X which is not numerically equivalent to the negative part in its divisorial Zariski…

This paper shows that for certain local topological properties, given a locally quasi-finite, flat and locally finitely presented map of schemes $f\colon X\to Y$, if $Y$ has the property, then so does $X$. We also show that being locally…

Let $K$ be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings $A$ over $K$, such that $H^0(A)$ is essentially of finite type over $K$, and…

In this paper we consider Gorenstein stable surfaces with $K^2_X=1$ and positive geometric genus. Extending classical results, we show that such surfaces admit a simple description as weighted complete intersection. We exhibit a wealth of…

We introduce three notion of tameness of the Nori fundamental group scheme for a normal quasiprojective variety $X$ over an algebraically closed field. It is proved that these three notions agree if $X$ admits a smooth completion with…

The Gauss map of a given projective variety is the rational map that sends a smooth point to the tangent space at that point, considered as a point of the Grassmann variety. The present paper aims to generalize a result by H. Kaji on Gauss…

We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the…

Let k be a field of characteristic zero. We show that the norm variety associated to a prime $\ell$ and an ordered sequence of invertible elements of k is geometrically retract rational. This generalizes a recent result of…

We prove that if $f:R \rightarrow S$ is a local homomorphism of noetherian local rings of finite flat dimension and $M$ is a non-zero finitely generated $S$-module whose Gorenstein flat dimension over $R$ is bounded by the difference of the…

Let $A$ be a two-dimensional excellent normal Gorenstein local domain. In this paper, we characterize elliptic ideals $I \subset A$ for its normal tangent cone $\overline{G}(I)$ to be Gorenstein. Moreover, we classify all those ideals in a…

The seminal theorem of I.J. Schoenberg characterizes positive definite (p.d.) kernels on the unit sphere $S^{n-1}$ invariant under the automorphisms of the sphere. We obtain two generalizations of this theorem for p.d. kernels on fiber…